On double cosets with the trivial intersection property and Kazhdan-Lusztig cells in $S_n$
作者： Thomas P. McDonough , Christos A. Pallikaros
关键词: Composition (combinatorics) 、 Type (model theory) 、 Coset 、 Normal subgroup 、 Lambda 、 Discrete mathematics 、 Hecke algebra 、 Symmetric group 、 Intersection 、 Mathematics
摘要: For a composition $lambda$ of $n$ our aim is to obtain reduced forms for all the elements in $w_{J(lambda)}$, the longest element standard parabolic subgroup $S_n$ corresponding $lambda$. We investigate how far this possible achieve by looking at elements form $w_{J(lambda)}d$, where $d$ prefix of an minimum length $(W_{J(lambda)},B)$ double coset with trivial intersection property, $B$ being parabolic subgroup of whose type `dual' that $W_{J(lambda)}$.
sci-hub.st 参考文章(22)
Francesco Brenti, Anders Björner, Combinatorics of Coxeter Groups ,(2010)
George Lusztig, Cells in Affine Weyl Groups Algebraic Groups and Related Topics. pp. 255- 287 ,(1985) , 10.2969/ASPM/00610255
Nanhua Xi, Representations of Affine Hecke Algebras ,(1994)
Gordon James, Adalbert Kerber, The representation theory of the symmetric group Cambridge University Press. ,(1984) , 10.1017/CBO9781107340732
Jian-Yi Shi, The Kazhdan-Lusztig cells in certain affine Weyl groups ,(1986)
Bruce Eli Sagan, The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions ,(1991)
Meinolf Josef Geck, Goetz Pfeiffer, Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras ,(2000)
George Lusztig, On a theorem of Benson and Curtis Journal of Algebra. ,vol. 71, pp. 490- 498 ,(1981) , 10.1016/0021-8693(81)90188-5
George Lusztig, Characters of reductive groups over a finite field ,(1984)
David Kazhdan, George Lusztig, Representations of Coxeter Groups and Hecke Algebras. Inventiones Mathematicae. ,vol. 53, pp. 165- 184 ,(1979) , 10.1007/BF01390031