Advertisement

Communications in Mathematical Physics

, Volume 224, Issue 2, pp 399–426 | Cite as

Quantum Invariant Measures

  • Nicolai Reshetikhin
  • Milen Yakimov

Abstract:

We derive an explicit expression for the Haar integral on the quantized algebra of regular functions ℂ q [K] on the compact real form K of an arbitrary simply connected complex simple algebraic group G. This is done in terms of the irreducible ✶-representations of the Hopf ✶-algebra ℂ q [K]. Quantum analogs of the measures on the symplectic leaves of the standard Poisson structure on K which are (almost) invariant under the dressing action of the dual Poisson algebraic group K are also obtained. They are related to the notion of quantum traces for representations of Hopf algebras. As an application we define and compute explicitly quantum analogs of Harish-Chandra c-functions associated to the elements of the Weyl group of G.

Keywords

Explicit Expression Invariant Measure Algebraic Group Weyl Group Regular Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Nicolai Reshetikhin
    • 1
  • Milen Yakimov
    • 1
  1. 1.Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720, USA.¶E-mail: reshetik@math.berkeley.edu; yakimov@math.berkeley.eduUS

Personalised recommendations