Hook interpolations

Ron M. Adin; Avital Frumkin; Yuval Roichman

doi:10.1016/S0021-8693(02)00642-7

Hook interpolations

Ron M. Adin, Avital Frumkin, Yuval Roichman

Department of Mathematics

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The hook components of V^⊗n interpolate between the symmetric power Symⁿ(V) and the exterior power ∧ⁿ(V). When V is the vector space of k × m matrices over C, we decompose the hook components into irreducible GL_k(C) × GL_m(C)-modules. In particular, classical theorems are proved as boundary cases. For the algebra of square matrices over C, a bivariate interpolation is presented and studied.

Original language	English
Pages (from-to)	543-562
Number of pages	20
Journal	Journal of Algebra
Volume	258
Issue number	2
DOIs	https://doi.org/10.1016/S0021-8693(02)00642-7
State	Published - 15 Dec 2002

Bibliographical note

Funding Information:
* Corresponding author. E-mail addresses: [email protected] (R.M. Adin), [email protected] (A. Frumkin), [email protected] (Y. Roichman). 1 Research was supported in part by the Israel Science Foundation, founded by the Israel Academy of Sciences and Humanities, and by internal research grants from Bar-Ilan University.

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abstract = "The hook components of V⊗n interpolate between the symmetric power Symn(V) and the exterior power ∧n(V). When V is the vector space of k × m matrices over C, we decompose the hook components into irreducible GLk(C) × GLm(C)-modules. In particular, classical theorems are proved as boundary cases. For the algebra of square matrices over C, a bivariate interpolation is presented and studied.",

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N2 - The hook components of V⊗n interpolate between the symmetric power Symn(V) and the exterior power ∧n(V). When V is the vector space of k × m matrices over C, we decompose the hook components into irreducible GLk(C) × GLm(C)-modules. In particular, classical theorems are proved as boundary cases. For the algebra of square matrices over C, a bivariate interpolation is presented and studied.

AB - The hook components of V⊗n interpolate between the symmetric power Symn(V) and the exterior power ∧n(V). When V is the vector space of k × m matrices over C, we decompose the hook components into irreducible GLk(C) × GLm(C)-modules. In particular, classical theorems are proved as boundary cases. For the algebra of square matrices over C, a bivariate interpolation is presented and studied.

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Hook interpolations

Abstract

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