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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Semisymmetric polynomials and the invariant theory of matrix vector pairs
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by Friedrich Knop
Represent. Theory 5 (2001), 224-266
Published electronically: August 15, 2001


We introduce and investigate a one-parameter family of multivariate polynomials $R_\lambda$. They form a basis of the space of semisymmetric polynomials, i.e., those polynomials which are symmetric in the variables with odd and even index separately. For two values of the parameter $r$, namely $r=\frac 12$ and $r=1$, the polynomials have a representation theoretic meaning related to matrix-vector pairs. In general, they form the semisymmetric analogue of (shifted) Jack polynomials. Our main result is that the $R_\lambda$ are joint eigenfunctions of certain difference operators. From this we deduce, among others, the Extra Vanishing Theorem, Triangularity, and Pieri Formulas.
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Bibliographic Information
  • Friedrich Knop
  • Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
  • MR Author ID: 103390
  • ORCID: 0000-0002-4908-4060
  • Email:
  • Received by editor(s): October 14, 1999
  • Received by editor(s) in revised form: May 12, 2001
  • Published electronically: August 15, 2001
  • Additional Notes: This work was partially supported by a grant of the NSF
  • © Copyright 2001 American Mathematical Society
  • Journal: Represent. Theory 5 (2001), 224-266
  • MSC (2000): Primary 33D55, 20G05, 39A70, 05E35
  • DOI:
  • MathSciNet review: 1857081