"Induced sign representations and characters of Hecke algebras"의 두 판 사이의 차이
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(피타고라스님이 이 페이지의 이름을 induced sign representations and characters로 바꾸었습니다.) |
Pythagoras0 (토론 | 기여) |
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| (사용자 3명의 중간 판 29개는 보이지 않습니다) | |||
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| − | + | ==introduction== | |
* http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=55223&date=2012-04-30 | * http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=55223&date=2012-04-30 | ||
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* Many combinatorial formulas for computations in the symmetric group Sn can be modified appropriately to describe computations in the Hecke algebra Hn(q), a deformation of C[Sn]. | * Many combinatorial formulas for computations in the symmetric group Sn can be modified appropriately to describe computations in the Hecke algebra Hn(q), a deformation of C[Sn]. | ||
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| − | + | ==induced sign characters== | |
* Unfortunately, the known formulas for induced sign characters of Sn are not among these. | * Unfortunately, the known formulas for induced sign characters of Sn are not among these. | ||
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* We will discuss evidence in favor of the conjecture, and relations to the chromatic quasi-symmetric functions of Shareshian and Wachs. | * We will discuss evidence in favor of the conjecture, and relations to the chromatic quasi-symmetric functions of Shareshian and Wachs. | ||
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| − | + | Given a partition \lambda=(\lambda_1,\cdots, \lambda_n) of n | |
| − | + | 1 define W_{\lambda}=S_{\lambda_1}\times S_{\lambda_2} \cdots \times S_{\lambda_k} | |
| − | + | 2 For each coset of the form wW_{\lambda}, | |
| − | + | define T_{wW_{\lambda}}=\sum_{v\in wW_{\lambda}}(-q)^{\ell(v)}T_{v} | |
| − | + | If we set q=1, we get a sum looks like (\sum_{w\in W} w_{\lambda} sgn(v)v) | |
| − | + | 3 Let H_n(q) act by lefy multiplication on coset sums T_{D} where D is of the form wW_{\lambda} | |
| − | + | 4 this left multiplication can be expressed as matrix multiplication | |
| − | + | Let \rho_{q}^{\lambda}(T_v)=matrix that correspondes to left multiplication by T_v. | |
| − | + | Let \rho^{\lambda}(v)=matrix corresponding to left multiplication by v. | |
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| − | + | the trace/character associated to representation \rho_{q}^{\lambda} are usually denoted by \epsilon_{q}^{\lambda} | |
| − | + | Q. What is a nice formula for \epsilon_{q}^{\lambda}(T_{v}) ? (open) | |
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| − | + | ==related items== | |
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| − | + | ==expositions== | |
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| − | + | [[분류:개인노트]] | |
| + | [[분류:quantum groups]] | ||
| + | [[분류:math and physics]] | ||
| + | [[분류:Hecke algebra]] | ||
| + | [[분류:migrate]] | ||
| − | + | ==메타데이터== | |
| − | + | ===위키데이터=== | |
| − | + | * ID : [https://www.wikidata.org/wiki/Q849798 Q849798] | |
| − | + | ===Spacy 패턴 목록=== | |
| − | + | * [{'LOWER': 'knot'}, {'LEMMA': 'theory'}] | |
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2021년 2월 17일 (수) 01:57 기준 최신판
introduction
- Many combinatorial formulas for computations in the symmetric group Sn can be modified appropriately to describe computations in the Hecke algebra Hn(q), a deformation of C[Sn].
induced sign characters
- Unfortunately, the known formulas for induced sign characters of Sn are not among these.
- For induced sign characters of Hn(q), we conjecture formulas which specialize at q=1 to formulas for induced sign characters of Sn.
- We will discuss evidence in favor of the conjecture, and relations to the chromatic quasi-symmetric functions of Shareshian and Wachs.
Given a partition \lambda=(\lambda_1,\cdots, \lambda_n) of n
1 define W_{\lambda}=S_{\lambda_1}\times S_{\lambda_2} \cdots \times S_{\lambda_k}
2 For each coset of the form wW_{\lambda},
define T_{wW_{\lambda}}=\sum_{v\in wW_{\lambda}}(-q)^{\ell(v)}T_{v}
If we set q=1, we get a sum looks like (\sum_{w\in W} w_{\lambda} sgn(v)v)
3 Let H_n(q) act by lefy multiplication on coset sums T_{D} where D is of the form wW_{\lambda}
4 this left multiplication can be expressed as matrix multiplication
Let \rho_{q}^{\lambda}(T_v)=matrix that correspondes to left multiplication by T_v.
Let \rho^{\lambda}(v)=matrix corresponding to left multiplication by v.
the trace/character associated to representation \rho_{q}^{\lambda} are usually denoted by \epsilon_{q}^{\lambda}
Q. What is a nice formula for \epsilon_{q}^{\lambda}(T_{v}) ? (open)
expositions
메타데이터
위키데이터
- ID : Q849798
Spacy 패턴 목록
- [{'LOWER': 'knot'}, {'LEMMA': 'theory'}]