On representation theory of partition algebras for complex reflection groups

DOI10.5802/alco.97zbMath1436.05130arXiv1812.04531OpenAlexW3106026413MaRDI QIDQ1985357

Shraddha Srivastava, Ashish Mishra

Publication date: 7 April 2020

Published in: Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.04531

zbMATH Keywords

Schur-Weyl dualitycomplex reflection groupsJucys-Murphy elementsTanabe algebras

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Ordinary representations and characters (20C15) Representations of finite symmetric groups (20C30) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Related Items (6)

The Gelfand–Tsetlin basis for infinite-dimensional representations of gln(C) ⋮ Multiparameter colored partition category and the product of the reduced Kronecker coefficients ⋮ Cutoff phenomenon for the warp-transpose top with random shuffle ⋮ On quasi Steinberg characters of complex reflection groups ⋮ The multiset partition algebra ⋮ Jucys–Murphy elements of partition algebras for the rook monoid

Cites Work

• Unnamed Item
• Unnamed Item
• The Okounkov-Vershik approach to the representation theory of \(G\sim S_n\)
• Partition algebras.
• A new approach to representation theory of symmetric groups
• Polynomial representations of \(\text{GL}_n\). With an appendix on Schensted correspondence and Littelmann paths by K. Erdmann, J. A. Green and M. Schocker.
• On the eigenvalues of representations of reflection groups and wreath products
• On the finite imprimitive unitary reflection groups
• Higher Specht polynomials for the complex reflection group \(G(r,p,n)\)
• On an algebraic approach to higher dimensional statistical mechanics
• Algebras in higher-dimensional statistical mechanics -- the exceptional partition (mean field) algebras
• \(G\)-colored partition algebras as centralizer algebras of wreath products
• A \(\lambda\)-ring Frobenius characteristic for \(G\wr S_n\)
• On the representation theory of wreath products of finite groups and symmetric groups
• A seminormal form for partition algebras
• On partition algebras for complex reflection groups.
• Colored-descent representations of complex reflection groups \(G(r,p,n)\).
• Partition algebras Pk(n) with 2k>n and the fundamental theorems of invariant theory for the symmetric group Sn
• Murnaghan-Nakayama Rules for Characters of Iwahori-Hecke Algebras of the Complex Reflection Groups G(r, p, n)
• Finite complex reflection groups
• TEMPERLEY-LIEB ALGEBRAS FOR NON-PLANAR STATISTICAL MECHANICS — THE PARTITION ALGEBRA CONSTRUCTION
• On the centralizer algebra of the unitary reflection group G(m,p,n)
• The partition algebra and the Potts model transfer matrix spectrum in high dimensions
• Finite Unitary Reflection Groups

This page was built for publication: On representation theory of partition algebras for complex reflection groups