On the decomposition numbers of the Hecke algebra of type Dn when n is even
作者： Jun Hu
DOI: 10.1016/J.JALGEBRA.2008.11.009
关键词: Pure mathematics 、 Schur algebra 、 Integer 、 Cellular algebra 、 Tensor product 、 Type (model theory) 、 Morita equivalence 、 Field (mathematics) 、 Mathematics 、 Hecke algebra
摘要: Abstract Let n ⩾ 4 be an even integer. K a field with char ≠ 2 and q invertible element in such that ∏ i = 1 − ( + ) 0 . In this paper, we study the decomposition numbers over of Iwahori–Hecke algebra H D type We obtain some equalities which relate its certain Schur elements various algebras A same parameter When , completely determine all numbers. The main tools used are Morita equivalence theorem established [J. Hu, for Hecke when is even, Manuscripta Math. 108 (2002) 409–430] twining character formulae Weyl modules tensor product two -Schur algebras.
elsevier.com
sci-hub.se 参考文章(32)
Stephen Donkin, The q-Schur algebra ,(1998)
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
Jun Hu, The number of simple modules for the Hecke algebras of type G(r,p,n): (with an appendix by Xiaoyi Cui) Journal of Algebra. ,vol. 321, pp. 3375- 3396 ,(2009) , 10.1016/J.JALGEBRA.2008.01.008
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
Richard Dipper, Gordon James, $q$-tensor space and $q$-Weyl modules Transactions of the American Mathematical Society. ,vol. 327, pp. 251- 282 ,(1991) , 10.1090/S0002-9947-1991-1012527-1
James A. Green, Polynomial representations of GLn Springer, Berlin, Heidelberg. pp. 124- 140 ,(1980) , 10.1007/BFB0090560
Susumu Ariki, Nicolas Jacon, Dipper–James–Murphy’s Conjecture for Hecke Algebras of Type Bn arXiv: Representation Theory. pp. 17- 32 ,(2010) , 10.1007/978-0-8176-4697-4_2
Meinolf Geck, On the representation theory of Iwahori-Hecke algebras of extended finite Weyl groups Representation Theory of The American Mathematical Society. ,vol. 4, pp. 370- 397 ,(2000) , 10.1090/S1088-4165-00-00093-5
Richard Dipper, Gordon James, Representations of Hecke algebras of type Bn Journal of Algebra. ,vol. 146, pp. 454- 481 ,(1992) , 10.1016/0021-8693(92)90078-Z
Richard Dipper, Gordon James, Eugene Murphy, Hecke Algebras of Type Bn
at Roots of Unity Proceedings of the London Mathematical Society. ,vol. s3-70, pp. 505- 528 ,(1995) , 10.1112/PLMS/S3-70.3.505