Noncommutative symmetric functions with matrix parameters

Autor: Alain Lascoux, Jean-Christophe Novelli, Jean-Yves Thibon

Publikováno v: Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AR,..., Iss Proceedings (2012)

We define new families of noncommutative symmetric functions and quasi-symmetric functions depending on two matrices of parameters, and more generally on parameters associated with paths in a binary tree. Appropriate specializations of both matrices

Externí odkaz: https://doaj.org/article/8e6d6f4be1f5484fbe8cddee4b460f8b

Factorization of Kazhdan–Lusztig Elements for Grassmanians

Autor: Alain Lascoux, Alexander Kirillov

Publikováno v: Combinatorial Methods in Representation Theory, K. Koike, M. Kashiwara, S. Okada, I. Terada and H.-F. Yamada, eds. (Tokyo: Mathematical Society of Japan, 2000)

We show that the Kazhdan–Lusztig basis elements $C_w$ of the Hecke algebra of the symmetric group, when $w \in S_n$ corresponds to a Schubert subvariety of a Grassmann variety, can be written as a product of factors of the form $T_i + f_j(v)$, wher

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::76b613e74764f3bca1c7e56c5a109032
https://doi.org/10.2969/aspm/02810143

Tableaux and Eulerian properties of the symmetric group

Autor: Alain Lascoux

Publikováno v: Schubert Calculus — Osaka 2012, H. Naruse, T. Ikeda, M. Masuda and T. Tanisaki, eds. (Tokyo: Mathematical Society of Japan, 2016)

The Ehresmann-Bruhat order on the symmetric group satisfies a symmetry property that we generalize to a directed graph with permutations as vertices, labeling edges with tableaux of a given shape.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8f00ea3fad48717fce5c286276a68abf
https://projecteuclid.org/euclid.aspm/1538623002

Branching rules for symmetric functions and sln basic hypergeometric series

Autor: S. Ole Warnaar, Alain Lascoux

Publikováno v: Advances in Applied Mathematics. 46:424-456

A one-parameter rational function generalisation Rλ(X;b) of the symmetric Macdonald polynomial and interpolation Macdonald polynomial is studied from the point of view of branching rules. We establish a Pieri formula, evaluation symmetry, principal

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4b027d9cbd974c3be12c77d5c4bb3ce2
https://doi.org/10.1016/j.aam.2010.01.012

Nonsymmetric interpolation macdonald polynomials and $ \mathfrak{g}\mathfrak{l}_n $ basic hypergeometric series

Autor: Eric M. Rains, S. Ole Warnaar, Alain Lascoux

Publikováno v: Transformation Groups. 14:613-647

The Knop-Sahi interpolation Macdonald polynomials are inhomogeneous and nonsymmetric generalisations of the well-known Macdonald polynomials. In this paper we apply the interpolation Macdonald polynomials to study a new type of basic hypergeometric s

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::6e9ad939ee8c930684de3db0a268a196
https://doi.org/10.1007/s00031-009-9061-1