Hook Interpolations

Adin, Ron M.; Frumkin, Avital; Roichman, Yuval

Hook Interpolations

Authors

Adin, Ron M.

Frumkin, Avital

Roichman, Yuval

Description

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.
23 pages; small changes