Invariant Differential Operators for Quantum Symmetric Spaces

Released on by Gail Letzter
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  • Invariant Differential Operators for Quantum Symmetric Spaces Book Detail

  • Author : Gail Letzter
  • Release Date : 2008
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 104
  • ISBN 13 : 0821841319
  • File Size : 79,79 MB
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Invariant Differential Operators for Quantum Symmetric Spaces by Gail Letzter PDF Summary

Book Description: This paper studies quantum invariant differential operators for quantum symmetric spaces in the maximally split case. The main results are quantum versions of theorems of Harish-Chandra and Helgason: There is a Harish-Chandra map which induces an isomorphism between the ring of quantum invariant differential operators and the ring of invariants of a certain Laurent polynomial ring under an action of the restricted Weyl group. Moreover, the image of the center under this map is the entire invariant ring if and only if the underlying irreducible symmetric pair is not of four exceptional types. In the process, the author finds a particularly nice basis for the quantum invariant differential operators that provides a new interpretation of difference operators associated to Macdonald polynomials.

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Consider representation theory associated to symmetric groups, or to Hecke algebras in type A, or to $q$-Schur algebras, or to finite general linear groups in n