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Hook lengths and representation theory

Published on:

2 April 2024

Primary Category:

Combinatorics

Paper Authors:

Chenglang Yang

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Key Details

Proves Amdeberhan's 2012 conjectures on hook-length and content generating functions

Formulas relate to dimensions of representations of symplectic/orthogonal groups

Uses vertex operators and symmetric function theory in proofs

Also provides some new combinatorial formulas beyond original conjectures

AI generated summary

Hook lengths and representation theory

This paper proves conjectures by Amdeberhan about combinatorial formulas involving the hook lengths and symplectic/orthogonal contents of integer partitions. These contents relate to representation theory of Lie groups. The key proof method uses vertex operators.

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