Kazhdan-Lusztig basis for generic Specht modules

Details Kazhdan-Lusztig basis for generic Specht modules Kazhdan-Lusztig basis for generic Specht modules

2010-12-10

arxiv.org/abs/1012.2195v1

Mathematics

Representation Theory

18 pages

Scientific paper

In this paper, we let $\Hecke$ be the Hecke algebra associated with a finite Coxeter group $W$ and with one-parameter, over the ring of scalars $\Alg=\mathbb{Z}(q, q^{-1})$. With an elementary method, we introduce a cellular basis of $\Hecke$ indexed by the sets $E_J (J\subseteq S)$ and obtain a general theory of "Specht modules". We provide an algorithm for $W\!$-graphs for the "generic Specht module", which associates with the Kazhdan and Lusztig cell ( or more generally, a union of cells of $W$ ) containing the longest element of a parabolic subgroup $W_J$ for appropriate $J\subseteq S$. As an example of applications, we show a construction of $W\!$-graphs for the Hecke algebra of type $A$.

Affiliated with

Also associated with

No associations

Rating

Kazhdan-Lusztig basis for generic Specht modules does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Kazhdan-Lusztig basis for generic Specht modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Kazhdan-Lusztig basis for generic Specht modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-106736