Modular representations and branching rules for affine and cyclotomic Yokonuma-Hecke algebras
作者： Weideng Cui , Jinkui Wan
DOI:
关键词:
摘要: We give an equivalence between a module category of the affine Yokonuma-Hecke algebra (associated with group $\mathbb{Z}/r\mathbb{Z}$) and its suitable counterpart for direct sum tensor products Hecke algebras type $A$. then develop several applications this result. In particular, simple modules associated cyclotomic are classified over algebraically closed field characteristic $p$ when does not divide $r$. The modular branching rules these obtained, they further identified crystal graphs integrable quantum algebras.
arxiv.org参考文章(38)
A. V. Zelevinsky, Induced representations of reductive ${\mathfrak {p}}$-adic groups. II. On irreducible representations of ${\rm GL}(n)$ Annales Scientifiques De L Ecole Normale Superieure. ,vol. 13, pp. 165- 210 ,(1980) , 10.24033/ASENS.1379
Andrey V. Zelevinsky, Representations of Finite Classical Groups: A Hopf Algebra Approach ,(1981)
Susumu Ariki, On the decomposition numbers of the Hecke algebra of $G(m, 1, n)$ Journal of Mathematics of Kyoto University. ,vol. 36, pp. 789- 808 ,(1996) , 10.1215/KJM/1250518452
I. N. Bernstein, A. V. Zelevinsky, Induced representations of reductive ${\mathfrak {p}}$-adic groups. I Annales Scientifiques De L Ecole Normale Superieure. ,vol. 10, pp. 441- 472 ,(1977) , 10.24033/ASENS.1333
Susumu Ariki, On the classification of simple modules for cyclotomic Hecke algebras of type $G(m,1,n)$ and Kleshchev multipartitions Osaka Journal of Mathematics. ,vol. 38, pp. 827- 837 ,(2001) , 10.18910/9564
Alexander Kleshchev, Linear and Projective Representations of Symmetric Groups ,(2009)
I. Grojnowski, Affine sl_p controls the representation theory of the symmetric group and related Hecke algebras arXiv: Representation Theory. ,(1999)
Weideng Cui, Cellularity of cyclotomic Yokonuma-Hecke algebras arXiv: Representation Theory. ,(2015)
M. Vazirani, Parameterizing Hecke Algebra Modules: Bernstein-Zelevinsky Multisegments, Kleshchev Multipartitions, and Crystal Graphs Transformation Groups. ,vol. 7, pp. 267- 303 ,(2002) , 10.1007/S00031-002-0014-1
A.S. Kleshchev, Branching Rules for Modular Representations of Symmetrical Groups I Journal of Algebra. ,vol. 178, pp. 493- 511 ,(1995) , 10.1006/JABR.1995.1362