A Littlewood-Richardson rule for the Macdonald inner product and bimodules over wreath products

Erik Carlsson; Anthony M. Licata

doi:10.1016/j.jalgebra.2015.05.022

A Littlewood-Richardson rule for the Macdonald inner product and bimodules over wreath products

Erik Carlsson^*
, Anthony M. Licata

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We prove a Littlewood-Richardson type formula for (sλ/μ,sν/κ)tk,t, the pairing of two skew Schur functions in the Macdonald inner product at q=t^k for positive integers k. This pairing counts graded decomposition numbers in the representation theory of wreath products of the algebra C[x]/xk and symmetric groups.

Original language	English
Pages (from-to)	520-537
Number of pages	18
Journal	Journal of Algebra
Volume	454
DOIs	https://doi.org/10.1016/j.jalgebra.2015.05.022
Publication status	Published - 15 May 2016

Access to Document

10.1016/j.jalgebra.2015.05.022

Cite this

@article{60706f017e52454abf34badc004ba622,

title = "A Littlewood-Richardson rule for the Macdonald inner product and bimodules over wreath products",

abstract = "We prove a Littlewood-Richardson type formula for (sλ/μ,sν/κ)tk,t, the pairing of two skew Schur functions in the Macdonald inner product at q=tk for positive integers k. This pairing counts graded decomposition numbers in the representation theory of wreath products of the algebra C[x]/xk and symmetric groups.",

keywords = "Categorification, Combinatorics, Littlewood Richardson, Macdonald inner product, Quantum algebra, Symmetric functions, Wreath products",

author = "Erik Carlsson and Licata, \{Anthony M.\}",

note = "Publisher Copyright: {\textcopyright} 2015.",

year = "2016",

month = may,

day = "15",

doi = "10.1016/j.jalgebra.2015.05.022",

language = "English",

volume = "454",

pages = "520--537",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - A Littlewood-Richardson rule for the Macdonald inner product and bimodules over wreath products

AU - Carlsson, Erik

AU - Licata, Anthony M.

PY - 2016/5/15

Y1 - 2016/5/15

N2 - We prove a Littlewood-Richardson type formula for (sλ/μ,sν/κ)tk,t, the pairing of two skew Schur functions in the Macdonald inner product at q=tk for positive integers k. This pairing counts graded decomposition numbers in the representation theory of wreath products of the algebra C[x]/xk and symmetric groups.

AB - We prove a Littlewood-Richardson type formula for (sλ/μ,sν/κ)tk,t, the pairing of two skew Schur functions in the Macdonald inner product at q=tk for positive integers k. This pairing counts graded decomposition numbers in the representation theory of wreath products of the algebra C[x]/xk and symmetric groups.

KW - Categorification

KW - Combinatorics

KW - Littlewood Richardson

KW - Macdonald inner product

KW - Quantum algebra

KW - Symmetric functions

KW - Wreath products

UR - https://www.scopus.com/pages/publications/84958999493

U2 - 10.1016/j.jalgebra.2015.05.022

DO - 10.1016/j.jalgebra.2015.05.022

M3 - Article

SN - 0021-8693

VL - 454

SP - 520

EP - 537

JO - Journal of Algebra

JF - Journal of Algebra

ER -

A Littlewood-Richardson rule for the Macdonald inner product and bimodules over wreath products

Abstract

Access to Document

Other files and links

Fingerprint

Cite this