Communications in Mathematical Physics

, Volume 195, Issue 2, pp 321–352

Quantum Weyl Reciprocity and Tilting Modules

Authors

  • Jie Du
    • School of Mathematics, University of New South Wales, Sydney 2052, Australia
  • Brian Parshall
    • Department of Mathematics, University of Virginia, Charlottesville, VA 22903-3199, USA
  • Leonard Scott
    • Department of Mathematics, University of Virginia, Charlottesville, VA 22903-3199, USA

DOI: 10.1007/s002200050392

Cite this article as:
Du, J., Parshall, B. & Scott, L. Comm Math Phys (1998) 195: 321. doi:10.1007/s002200050392

Abstract:

Quantum Weyl reciprocity relates the representation theory of Hecke algebras of type A with that of q-Schur algebras. This paper establishes that Weyl reciprocity holds integrally (i. e., over the ring ℤ[q, q− 1] of Laurent polynomials) and that it behaves well under base-change. A key ingredient in our approach involves the theory of tilting modules for q-Schur algebras. New results obtained in that direction include an explicit determination of the Ringel dual algebra of a q-Schur algebra in all cases. In particular, in the most interesting situation, the Ringel dual identifies with a natural quotient algebra of the Hecke algebra.

Copyright information

© Springer-Verlag Berlin Heidelberg 1998