scholarly journals Peak algebras, paths in the Bruhat graph and Kazhdan–Lusztig polynomials

2017 ◽  
Vol 304 ◽  
pp. 539-582 ◽  
Author(s):  
Francesco Brenti ◽  
Fabrizio Caselli
Keyword(s):  
Bruhat Graph ◽  
Lusztig Polynomials

scholarly journals Peak algebras, paths in the Bruhat graph and Kazhdan-Lusztig polynomials

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Francesco Brenti ◽  
Fabrizio Caselli
Keyword(s):  
Combinatorial Formula ◽  
Quasisymmetric Functions ◽  
International Audience ◽  
Bruhat Graph ◽  
Lusztig Polynomials

International audience We obtain a nonrecursive combinatorial formula for the Kazhdan-Lusztig polynomials which holds in complete generality and which is simpler and more explicit than any existing one, and which cannot be linearly simplified. Our proof uses a new basis of the peak subalgebra of the algebra of quasisymmetric functions. On montre une formule combinatoire pour les polynômes de Kazhdan-Lusztig qui est valable en toute généralité. Cette formule est plus simple et plus explicite que toutes les autres formules connues; de plus, elle ne peut pas être simplifiée linéairement. La preuve utilise une nouvelle base pour la sous-algèbre des sommets de l’algèbre des fonctions quasi-symmetriques.

Kazhdan-Lusztig polynomials and canonical basis

1998 ◽  
Vol 3 (4) ◽  
pp. 321-336 ◽  
Author(s):  
I. B. Frenkel ◽  
M. G. Khovanov ◽  
A. A. Kirillov
Keyword(s):  
Canonical Basis ◽  
Lusztig Polynomials

The Hecke Algebra and Kazhdan–Lusztig Polynomials

2020 ◽  
pp. 39-58
Author(s):  
Ben Elias ◽  
Shotaro Makisumi ◽  
Ulrich Thiel ◽  
Geordie Williamson
Keyword(s):  
Hecke Algebra ◽  
Lusztig Polynomials

scholarly journals Formulas for multi-parameter classes of Kazhdan–Lusztig polynomials in S(n)

2006 ◽  
Vol 306 (8-9) ◽  
pp. 711-725
Author(s):  
F. Caselli ◽  
M. Marietti
Keyword(s):  
Lusztig Polynomials

scholarly journals Kazhdan–Lusztig polynomials and subexpressions

2021 ◽  
Vol 568 ◽  
pp. 181-192
Author(s):  
Nicolas Libedinsky ◽  
Geordie Williamson
Keyword(s):  
Lusztig Polynomials

scholarly journals Casselman’s Basis of Iwahori Vectors and Kazhdan–Lusztig Polynomials

2019 ◽  
Vol 71 (6) ◽  
pp. 1351-1366
Author(s):  
Daniel Bump ◽  
Maki Nakasuji
Keyword(s):  
Representation Theory ◽  
Functional Equations ◽  
Transition Matrix ◽  
Principal Series ◽  
Surprising Result ◽  
Transition Matrices ◽  
Natural Basis ◽  
Series Representations ◽  
The Matrix ◽  
Lusztig Polynomials

AbstractA problem in representation theory of $p$-adic groups is the computation of the Casselman basis of Iwahori fixed vectors in the spherical principal series representations, which are dual to the intertwining integrals. We shall express the transition matrix $(m_{u,v})$ of the Casselman basis to another natural basis in terms of certain polynomials that are deformations of the Kazhdan–Lusztig R-polynomials. As an application we will obtain certain new functional equations for these transition matrices under the algebraic involution sending the residue cardinality $q$ to $q^{-1}$. We will also obtain a new proof of a surprising result of Nakasuji and Naruse that relates the matrix $(m_{u,v})$ to its inverse.

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