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arXiv · 2211.15252

Some Restriction Coefficients for the Trivial and Sign Representations

Sridhar P. Narayanan·Digjoy Paul·Amritanshu Prasad·Shraddha Srivastava
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Abstract

We use character polynomials to obtain a positive combinatorial interpretation of the multiplicity of the sign representation in irreducible polynomial representations of $GL_n(\mathbb{C})$ indexed by two-column and hook partitions. Our method also yields a positive combinatorial interpretation for the multiplicity of the trivial representation of $S_n$ in an irreducible polynomial representation indexed by a hook partition.

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Sridhar P. Narayanan, Digjoy Paul, Amritanshu Prasad, Shraddha Srivastava. 2022-11-28. Some Restriction Coefficients for the Trivial and Sign Representations. https://arxiv.org/abs/2211.15252

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