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Crystal bases and simple modules for Hecke algebras of type G(p,p,n) | | Jun Hu
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27 Jun 2005 | | Subject: | Representation Theory; Quantum Algebra MSC-class: 20C08, 20C20 | math.RT math.QA | | Abstract: | We apply the crystal bases theory of Fock spaces over quantum affine algebras to the modular representations of the cyclotomic Hecke algebras of type $G(p,p,n)$. This yields 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 formula for the number of simple modules over these cyclotomic Hecke algebras. Our formula generalizes, in the special case where $p=2$, earlier results of [M. Geck, Represent. Theory 4 (2000) 370-397] on the Hecke algebras of type $D_n$. | | Source: | arXiv, math.RT/0506555 | | Services: | Forum | Review | PDF | Favorites | |
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