Finite dimensional representations of symplectic reflection algebras associated to wreath products II
| dc.creator | Montarani, Silvia | |
| dc.date | 2005-01-11 | |
| dc.date.accessioned | 2026-07-07T05:15:58Z | |
| dc.date.available | 2026-07-07T05:15:58Z | |
| dc.description | This note extends some results of a previous paper (math.RT/0403250) about finite dimensional representations of the wreath product symplectic reflection algebra H(k,c,N,G) of rank N attached to a finite subgroup G of SL(2,C) (here k is a number and c a class function on the set of nontrivial elements of G). Specifically, let N'=(N_1,...,N_r) be a partition of N. Consider W=W_1\otimes >...\otimes W_r an irreducible representation of S_N'=S_{N_1}\times ...\times S_{N_r}\subset S_N s.t. W_i has rectangular Young diagram for any i and let {Y_i}, i=1,...,r be a collection of irreducible non isomorphic representation of the rank 1 algebra B=H(c_0,1,G) s.t. Ext^1_B(Y_i, Y_j)=0 for any i\neq j. Consider the module M'=W\otimes Y, where Y=Y_1^{N_1}\otimes ...\otimes Y_r^{N_r}, over the subalgebra S_N'#B^N \subset S_N#B^N= H(0,c_0,N,G) and form the induced module M over H(0,c_0,N,G). We show that M can be uniquely deformed along a linear subspace of codimension r in the space of the parameters (k,c) passing through c_0. This result implies the main result of math.RT/0403250 as a particular case, the case of the trivial partition N'=(N). | |
| dc.description | 10 pages, Latex | |
| dc.identifier | https://arxiv.org/abs/math/0501156 | |
| dc.identifier | http://arxiv.org/abs/math/0501156 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73816 | |
| dc.subject | Representation Theory | |
| dc.title | Finite dimensional representations of symplectic reflection algebras associated to wreath products II | |
| dc.type | text |