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Quantized flag manifolds and non-restricted modules over quantum groups at roots of unity

Toshiyuki Tanisaki

Abstract

We give a proof of Lusztig's conjectural multiplicity formula for non-restricted modules over the De Concini-Kac type quantized enveloping algebra at the $\ell$-th root of unity, where $\ell$ is an odd prime power satisfying certain reasonable conditions.

Quantized flag manifolds and non-restricted modules over quantum groups at roots of unity

Abstract

We give a proof of Lusztig's conjectural multiplicity formula for non-restricted modules over the De Concini-Kac type quantized enveloping algebra at the -th root of unity, where is an odd prime power satisfying certain reasonable conditions.

Paper Structure

This paper contains 41 sections, 455 equations.

Table of Contents

  1. Introduction
  2. Quantum groups
  3. Simple Lie algebra
  4. Quantized enveloping algebra
  5. Harish-Chandra center
  6. Quantized coordinate algebra
  7. Induction functor
  8. $R$-matrix
  9. ${\mathcal{O}}$-modules on the quantized flag manifolds
  10. Quantized partial flag manifold
  11. Another description of quantized partial flag manifold
  12. Equivariant ${\mathcal{O}}$-modules
  13. Inverse and direct images
  14. $D$-modules on the quantized flag manifolds
  15. $D$-modules
  16. ...and 26 more sections

Theorems & Definitions (25)

  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • ...and 15 more