Crystal bases and simple modules for Hecke algebras of type G(p,p,n)
| dc.creator | Hu, Jun | |
| dc.date | 2005-06-27 | |
| dc.date | 2007-02-20 | |
| dc.date.accessioned | 2026-07-07T07:47:30Z | |
| dc.date.available | 2026-07-07T07:47:30Z | |
| dc.description | We apply the crystal basis theory for Fock spaces over quantum affine algebras to the modular representations of the cyclotomic Hecke algebras of type $G(p,p,n)$. This yields a classification of simple modules over these cyclotomic Hecke algebras in the non-separated case, generalizing our previous work [J. Hu, J. Algebra 267 (2003) 7-20]. The separated case was completed in [J. Hu, J. Algebra 274 (2004) 446--490]. Furthermore, we use Naito--Sagaki's work [S. Naito & D. Sagaki, J. Algebra 251 (2002) 461--474] on Lakshmibai--Seshadri paths fixed by diagram automorphisms to derive explicit formulas for the number of simple modules over these Hecke algebras. These formulas generalize earlier results of [M. Geck, Represent. Theory 4 (2000) 370-397] on the Hecke algebras of type $D_n$ (i.e., of type $G(2,2,n)$). | |
| dc.description | 38 pages | |
| dc.identifier | https://arxiv.org/abs/math/0506555 | |
| dc.identifier | http://arxiv.org/abs/math/0506555 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124189 | |
| dc.subject | Representation Theory | |
| dc.subject | Quantum Algebra | |
| dc.subject | 20C08, 20C20 | |
| dc.title | Crystal bases and simple modules for Hecke algebras of type G(p,p,n) | |
| dc.type | text |