Unit doublet - Revision history

en>PWilkinson: Link disambiguation

2014-07-06T10:51:40Z

Link disambiguation

← Older revision		Revision as of 12:51, 6 July 2014
Line 1:		Line 1:
	In [[mathematics]], the '''Jucys–Murphy elements''' in the [[group algebra]] <math>\mathbb{C} [S_n] </math> of the [[symmetric group]], named after [[Algimantas Adolfas Jucys]] and G. E. Murphy, are defined as a sum of [[transposition (mathematics)\|transposition]]s by the formula:

	~~:<math>X_1=0, ~~~ X_k= (1 k)+ (2 k)+\cdots+(k-1\ k), ~~~ k=2,\dots,n. </math>~~

	~~They play an important role in~~ the ~~[[representation theory]] of~~ the ~~[[symmetric group]]~~.		You want to discover much more about how to deal with your auto repairs, and you happen to be kind of lost on the subject. Like many individuals, when something takes place, you just hope that the bill is less expensive than you thought. To discover more, consider glancing at: [http://www.prweb.com/releases/windstar-used-gearbox/ford-used-transmission/prweb10904401.htm like]. Take command of your information base concerning auto repair, and place your self in the position to make a properly-informed decision.<br><br>Check the transmission fluid every two to three months. Let your engine run and open the hood of your car. Use the transmission dipstick to verify the fluid levels. If there is not enough fluid in your transmission you probably have a leak somewhere in your technique. It is greatest to take the vehicle to a mechanic so he can find the leak.<br><br>It is a excellent notion to use referrals to discover a decent mechanic. Get suggestions from family and buddies. You can inquire about value, work high quality and all round satisfaction. Visiting [http://www.prweb.com/releases/used-jeep-transmissions/jeep-transmissions-sale/prweb11423713.htm jeep transmissions] possibly provides tips you can tell your brother. Men and women will let you know if their experiences have been great or undesirable and how honest the auto repair shop was with them.<br><br>Preventative maintenance is quite crucial if you personal a automobile. Do not hesitate to devote money on the tools you need to inspect and sustain your car or getting a mechanic look at your auto regularly. Maintaining your car frequently could assist you save a lot on repairs or towing if your automobile breaks down.<br><br>If you are having operate done on your auto, make confident you get a written estimate beforehand. The estimate ought to contain what is becoming repaired, the parts that will be required and the anticipated expense for labor. It ought to also say that they will get in touch with for your approval prior to doing any extra operate which exceeds the amount or time specified.<br><br>It is time to consider about your options when it comes to auto repairs. Make confident you consider about the suggestions that have been talked about in this report so that you can select what you should do. Should people wish to discover more about [https://www.youtube.com/watch?v=s4VmTu0KlXg best 700r4 transmission rebuild], there are many on-line databases you should pursue. You can now take care of your auto repairs the best way possible..<br><br>If you have any issues about wherever and how to use [http://www.fizzlive.com/magnificentwoma27 health current events], you can get hold of us at our web page.

	~~==Properties==~~
	~~They generate a commutative subalgebra of <math>\mathbb{C}~~ [ ~~S_n] <~~/~~math>~~. ~~Moreover,~~
	~~''X''<sub>''n''<~~/~~sub> commutes with all elements~~ of <~~math~~>~~\mathbb{C} [S_{n-1}]~~ <~~/math~~>.

	~~The vectors~~ of the ~~Young basis are eigenvectors for~~ the ~~action of ''X''<sub>''n''</sub>~~. ~~For any [[standard Young tableau]] ''U'' we~~ have:

	:<~~math~~>~~X_k v_U =c_k(U) v_U, ~~~ k=1,\dots,n, </math>~~

	~~where ''c''~~<~~sub~~>~~''k''</sub>(''U'')~~ is ~~the ''content'' ''b'' − ''~~a~~'' of the cell (''~~a'',~~ ''b'') occupied by ''k'' in the standard Young tableau ''U''~~.

	~~'''Theorem''' (Jucys)~~: ~~The [[Center (algebra)\|center~~]~~] <math>Z(\mathbb{C} [S_n])</math> of~~ the ~~group algebra~~ <~~math~~>~~\mathbb{C} [S_n]~~ <~~/math~~> ~~of the symmetric group~~ is ~~generated by~~ the ~~[[symmetric polynomial]]s in the elements ''X~~<~~sub~~>k<~~/sub~~>''.

	~~'''Theorem''' (Jucys): Let ''t''~~ be ~~a formal variable commuting with everything, then~~ the ~~following identity~~ for ~~polynomials~~ in ~~variable ''t''~~ with ~~values in~~ the ~~group algebra~~ <~~math~~>~~\mathbb{C} [S_n]~~ <~~/math~~> ~~holds true:~~

	~~:<math> (t+X_1) (t+X_2) \cdots (t+X_n)= \sum_{\sigma \~~in ~~S_n} \sigma t^{\text{number of cycles of }\sigma}~~.~~</math>~~

	~~'''Theorem''' ([[Okounkov]]–[~~[~~Vershik]])~~: ~~The subalgebra of <math>\mathbb{C} [S_n] <~~/~~math> generated by the centers~~

	~~: <math> Z(\mathbb{C} [ S_1~~]), ~~Z(\mathbb{C} [ S_2]), \ldots, Z(\mathbb{C} [ S_{n~~-~~1}]), Z(\mathbb{C} [S_n]) </math>~~

	~~is exactly~~ the ~~subalgebra generated by the Jucys–Murphy elements ''X~~<~~sub~~>k<~~/sub~~>~~''.~~

	~~==See also==~~
	* [~~[Representation theory of the symmetric group]]~~
	* [[Young symmetrizer]]

	~~==References==~~
	*{{Citation
	~~\|title=A New Approach to the Representation Theory of the Symmetric Groups. 2~~
	~~\|authorlink1=Okounkov~~
	~~\|first1=Andrei \|last1=Okounkov~~
	~~\|authorlink2=Vershik~~
	~~\|first2=Anatoly \|last2=Vershik~~
	~~\|year=2004~~
	~~\|volume=307~~
	~~\|journal=Zapiski Seminarod POMI (In Russian) v.~~
	~~\|arxiv = math.RT~~/~~0503040~~
	~~\|postscript= (revised English version). }}~~

	*{{citation
	~~\|title=Symmetric polynomials and the center of the symmetric group ring~~
	~~\|authorlink1=Algimantas Adolfas Jucys~~
	~~\|first1=Algimantas Adolfas \|last1=Jucys~~
	~~\| year=1974 \| journal=Rep. Mathematical Phys. \| volume=5 \| issue=1 \| pages=107–112~~
	~~\| doi=10.1016~~/~~0034-4877(74)90019-6~~
	}}

	*{{citation
	~~\|title=On the Young operators of the symmetric group~~
	~~\|authorlink1=Algimantas Adolfas Jucys~~
	~~\|first1=Algimantas Adolfas \|last1=Jucys~~
	~~\| year=1966 \| journal=Lietuvos Fizikos Rinkinys \| volume=6 \| pages=163–180~~
	}}

	*{{citation
	~~\|title=Factorization of Young projection operators for the symmetric group~~
	~~\|authorlink1=Algimantas Adolfas Jucys~~
	~~\|first1=Algimantas Adolfas \|last1=Jucys~~
	~~\| year=1971 \| journal=Lietuvos Fizikos Rinkinys \| volume=11 \| pages=5–10~~
	}}

	*{{citation
	~~\|title=A new construction of Young's seminormal representation of the symmetric group~~
	~~\|first1=G~~. E. ~~\|last1=Murphy~~
	~~\| year=1981 \| journal=J. Algebra \| volume=69 \| pages=287–297~~
	~~\|doi=10.1016~~/~~0021-8693(81)90205-2~~
	~~\|issue=2~~
	}}

	~~{{DEFAULTSORT:Jucys-Murphy Element}}~~
	~~[[Category:Permutation groups~~]]
	~~[[Category:Representation theory]]~~
	~~[[Category:Symmetry]]~~
	~~[[Category:Representation theory~~ of ~~finite groups]]~~
	~~[[Category:Symmetric functions]]~~

en>Duoduoduo: wikilink

2013-08-31T16:23:46Z

wikilink

Show changes

en>Rgdboer: /* References */ cat

2012-08-29T21:28:30Z

References: cat

New page

Whether you wish to make an old couch look brand-new or merely wish to spruce up the interiors of your living room, sofa pillows that are offered in unimaginable colors, designs, and patterns, nowadays, are precisely what you need. Add a couple of vibrant and bright toss pillows and you will certainly be astonished at the type of result they have on your living-room. And the very best part about them is that they are quite pocket-friendly, as well. Pillow experts warn that when choosing the right bed pillow, clients need to be on the watch out for pillows that contain fibers that can set off allergies. Bed pillows that contain feathers or wool for example, could trigger allergic reactions in some people who are already conscious these fibers. For this reason, it is essential to read the label that describes the types of fibers that a pillow includes prior to you buy it. Start with a pillow that looks 'best' for you. Lie down the method you typically slip the pillow and [http://diypillow.com do it yourself pillow] under your neck. Do not hurry yourself to decide. Take a minute to 'settle'. Turn around and try your favorite resting postures. Rate the pillow for comfort level. Orthopedic Pillows for the Taking a trip Individual In general, if you like to sleep on your tummy, a softer and flatter pillow is probably your best bet. A softer pillow helps relieve tension on your neck that a firmer pillow might [http://www.squidoo.com/search/results?q=enhance enhance]. Sleeping on your tummy is normally accompanied by a twisting of the neck. A firm pillow might likewise include stress on the neck by compeling your head up. So, for a stomach sleeper to have the most comfy sleep, select a soft, flat pillow, or a pillow that permits you to add or remove the fill to personalize your comfort. Excellent choices for the tummy sleeper might consist of a Dacron Polyester filled pillow, or the Eco-Basics Pillow Push the pillows into the washing machine and then let the machine surface filling with water. The water setting should be on the greatest water level setting readily available. After the machine fills, inspect to see if the pillows have actually risen in the machine, which is possible from air captured between the feathers. Force the pillows beneath the water. Set the device for a brief wash time, or about five minutes. Use the GENTLE setting for BOTH the wash and spin cycles. With the feather pillows out of the washing device, add half the quantity of cleaning agent that you would use for a full wash, and then fill the machine halfwaywarm water. Upset the water to completely mix the detergent by either utilizing your hand to swish the water. As previously discussed, you have to continuously keep an eye on the pillows, pushing them back under the water each to 2 minutes (with the device off, naturally) during both the wash and rinse cycles. After the last gentle spin cycle, reset the machine to the normal/fast spin background and rerun simply the spin cycle to extract more water from the pillows If it is extravagant comfort and support you are after, Kerry advises the Flexi Pillow, an all rounder which costs $149. Pillows and the bed room in general is frequently a rich environment for allergen. These allergen live off fungi discovered in pillows. After the allergen eat, they leave allergen feces. The fungi also soak up the dust mite feces. Humans also supply skin flakes, bodily fluids and germs that allergen and fungi feed off. They likewise add 20 gallons of sweat into their bed when individuals rest. This adds to the zoo impact, allowing even more microbes to breed. It is a relatively common complaint that the back, neck and arms of a nursing mom are most strained while nursing a baby, however with a correct breastfeeding pillow such problems could be a distant memory. Numerous of these pillows are ergonomically designed to guarantee that they protect the nursing mother from the most common complaint, pain in the back. The quality of these pillows improves with time. It gets better with time and helps you have a nice noise sleep. Last long and with time it continues improving with time. Memory foam pillow have a great quality. It would be a terrific financial investment for your wellness and you would never ever be sorry for after you have gotten it, especially when you have aching neck it would not leave you disappointed. Air Travel Precautions Considering that the devices used for this process is typically costly, many people don't have direct to garment printers in their houses. Nevertheless, the process is becoming more popular and because the water-based ink does not lie on top of fabric like a regular heat transfer does. Images printed with digital garment printing continue to be resilient and soft. The image actually becomes part of the material because the inks permeate the fibers! To discover a digital direct to garment printer in your area, begin by checking with screen printers to see if they offer the process. The primary reason professionals alert versus placing pillows in a child's baby crib is the risk of suffocation. She won't have the neck strength to move her head and draw her mouth and nose away if a baby gets her face pressed into a pillow. A pillow in an open case postures a threat also, since an infant could potentially get her head stuck inside the case. Infants are likewise sensitive to allergens like allergen, down and feathers, and sleeping on these materials all night can cause extreme allergies. When to Present Pillows In case you're unclear just what travel pillow to buy then the best shop to obtain started on might well be Amazon because of their item evaluation procedure together with the top notch shipping and shipping. Amazon provides a really safe and safe and secure technique to buy online this implies you won't need to fret about anything. So I stopped traveling for a long time because of that however after several years I requiremented to go to a specific destination for company factors. As Soon As I have actually arrived at the worldwide flight terminal I spotted a couple of individuals grasping a u-shaped travel pillow and yes it got me curious. I asked an individual close to me regarding the pillow in which he stated it was a neck pillow for travel helping him to go to sleep. Ways to Bring Travel Files