Hook Interpolations

Details Hook Interpolations Hook Interpolations

2001-09-04

arxiv.org/abs/math/0109023v2

J. Algebra 258 (2002), 543--562

Mathematics

Representation Theory

23 pages; small changes

Scientific paper

The hook components of $V^{\otimes n}$ interpolate between the symmetric power $\sym^n(V)$ and the exterior power $\wedge^n(V)$. When $V$ is the vector space of $k\times m$ matrices over $\bbc$, we decompose the hook components into irreducible $GL_k(\bbc)\times GL_m(\bbc)$-modules. In particular, classical theorems are proved as boundary cases. For the algebra of square matrices over $\bbc$, a bivariate interpolation is presented and studied.

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