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KRONECKER COEFFICIENTS FOR (DUAL) SYMMETRIC INVERSE SEMIGROUPS

Part of: Algebraic combinatorics Semigroups

Published online by Cambridge University Press:  13 September 2024

VOLODYMYR MAZORCHUK Open the ORCID record for VOLODYMYR MAZORCHUK [Opens in a new window]  and
SHRADDHA SRIVASTAVA Open the ORCID record for SHRADDHA SRIVASTAVA [Opens in a new window]
VOLODYMYR MAZORCHUK
Affiliation:
Department of Mathematics, Uppsala University, Box. 480, SE-75106 Uppsala, Sweden e-mail: [email protected]
SHRADDHA SRIVASTAVA*
Affiliation:
Department of Mathematics, Indian Institute of Technology, Dharwad, Karnataka 580007, India
*
e-mail: [email protected]
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Abstract

We study analogues of Kronecker coefficients for symmetric inverse semigroups, for dual symmetric inverse semigroups and for the inverse semigroups of bijections between subquotients of finite sets. In all cases, we reduce the problem of determination of such coefficients to some group-theoretic and combinatorial problems. For symmetric inverse semigroups, we provide an explicit formula in terms of the classical Kronecker and Littlewood–Richardson coefficients for symmetric groups.

Keywords

Kronecker coefficientsinverse semigroupspartition algebras

MSC classification

Primary: 20M30: Representation of semigroups; actions of semigroups on sets
Secondary: 05E10: Combinatorial aspects of representation theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 118 , Issue 1 , February 2025 , pp. 65 - 90
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by James East

The first author is partially supported by the Swedish Research Council. The second author was supported by DST INSPIRE faculty fellowship ref. no. DST/INSPIRE/04/2021/000268.

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