Tiling branching multiplicity spaces with GL2 pattern blocks

TL;DR

This paper explores how the combinatorics of GL(2) representations can be used to understand branching rules for complex classical groups, including GL(n), symplectic, and orthogonal groups, revealing new structural insights.

Contribution

It introduces a novel combinatorial framework for analyzing branching multiplicity spaces using GL(2) pattern blocks, extending to symplectic and orthogonal groups.

Findings

Established a combinatorial description of branching multiplicities for GL(n) using GL(2) patterns

Extended the framework to symplectic and orthogonal groups

Provided new insights into the structure of classical group restrictions

Abstract

We study branching multiplicity spaces of complex classical groups in terms of GL(2) representations. In particular, we show how combinatorics of GL(2) representations are intertwined to make branching rules under the restriction of GL(n) to GL(n-2). We also discuss analogous results for the symplectic and orthogonal groups.