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On Tensor Products of Polynomial Representations

Published online by Cambridge University Press:  20 November 2018

Kevin Purbhoo  and
Stephanie van Willigenburg
Kevin Purbhoo
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2. e-mail: kevinp@math.ubc.ca e-mail: steph@math.ubc.ca
Stephanie van Willigenburg
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2. e-mail: kevinp@math.ubc.ca e-mail: steph@math.ubc.ca
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Abstract

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We determine the necessary and sufficient combinatorial conditions for which the tensor product of two irreducible polynomial representations of $\text{GL}\left( n,\,\mathbb{C} \right)$ is isomorphic to another. As a consequence we discover families of Littlewood–Richardson coefficients that are non-zero, and a condition on Schur non-negativity.

Keywords

05E0505E1020C30polynomial representationsymmetric functionLittlewood–Richardson coefficientSchur non-negative

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 4 , 01 December 2008 , pp. 584 - 592
Copyright
Copyright © Canadian Mathematical Society 2008

References

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