Noncommutative LR coefficients and crystal reflection operators

Richmond, Edward; Tewari, Vasu

doi:10.5802/alco.155

Richmond, Edward ¹; Tewari, Vasu ²

¹ Oklahoma State University Department of Mathematics Stillwater OK 74708, USA
² University of Pennsylvania Department of Mathematics Philadelphia PA 19104, USA

Algebraic Combinatorics, Volume 4 (2021) no. 1, pp. 145-162.

Abstract

We relate noncommutative Littlewood–Richardson coefficients of Bessenrodt–Luoto–van Willigenburg to classical Littlewood–Richardson coefficients via crystal reflection operators. A key role is played by the combinatorics of frank words.

Received: 2019-08-19
Revised: 2020-08-11
Accepted: 2020-10-06
Published online: 2021-02-16

DOI: 10.5802/alco.155

Classification: 05E05, 05A05, 05E10, 20C30
Keywords: Crystal operator, Littlewood–Richardson coefficient, noncommutative symmetric function, symmetric function, Schur function.

Author's affiliations:

Richmond, Edward ¹; Tewari, Vasu ²

¹ Oklahoma State University Department of Mathematics Stillwater OK 74708, USA
² University of Pennsylvania Department of Mathematics Philadelphia PA 19104, USA

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Richmond, Edward; Tewari, Vasu. Noncommutative LR coefficients and crystal reflection operators. Algebraic Combinatorics, Volume 4 (2021) no. 1, pp. 145-162. doi : 10.5802/alco.155. https://alco.centre-mersenne.org/articles/10.5802/alco.155/

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