Invariant algebras and major indices for classical Weyl groups

DOI10.1112/S0024611503014552zbMath1067.05077OpenAlexW2097581076MaRDI QIDQ4812524

Riccardo Biagioli, Fabrizio Caselli

Publication date: 23 August 2004

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/s0024611503014552

zbMATH Keywords

major indexMahonian statisticdescent statisticdiagonal invariant algebraEuler--Mahonian statistics

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Symmetric functions and generalizations (05E05) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Actions of groups on commutative rings; invariant theory (13A50)

Related Items

Signed Mahonian polynomials for classical Weyl groups ⋮ A descent basis for the coinvariant algebra of type \(D\) ⋮ Diagonal invariants and the refined multimahonian distribution. ⋮ Odd and even major indices and one-dimensional characters for classical Weyl groups ⋮ Signed Mahonian on parabolic quotients of colored permutation groups ⋮ Enumerating wreath products via Garsia-Gessel bijections ⋮ Weighted enumerations on projective reflection groups ⋮ Signed Euler-Mahonian identities ⋮ A combinatorial proof of a symmetry of \((t,q)\)-Eulerian numbers of type \(B\) and type \(D\) ⋮ Equidistribution of negative statistics and quotients of Coxeter groups of type \(B\) and \(D\) ⋮ Colored-descent representations of complex reflection groups \(G(r,p,n)\). ⋮ Projective reflection groups. ⋮ Signed Mahonians ⋮ Parabolically induced functions and equidistributed pairs ⋮ Equi-distribution over descent classes of the hyperoctahedral group ⋮ Signed Mahonian polynomials for major and sorting indices ⋮ Hecke group algebras as quotients of affine Hecke algebras at level 0. ⋮ Signed words and permutations. V: A sextuple distribution ⋮ Signed words and permutations, I: A fundamental transformation ⋮ Advanced determinant calculus: a complement