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The Koszul complex and a certain induced module for a quantum group

Toshiyuki Tanisaki

Abstract

We give a description of a certain induced module for a quantum group of type $A$. Together with our previous results this gives a proof of Lusztig's conjectural multiplicity formula for non-restricted modules over the De Concini-Kac type quantized enveloping algebra of type $A_n$ at the $\ell$-th root of unity, where $\ell$ is an odd integer satisfying $(\ell,n+1)=1$ and $\ell> n+1$.

The Koszul complex and a certain induced module for a quantum group

Abstract

We give a description of a certain induced module for a quantum group of type . Together with our previous results this gives a proof of Lusztig's conjectural multiplicity formula for non-restricted modules over the De Concini-Kac type quantized enveloping algebra of type at the -th root of unity, where is an odd integer satisfying and .
Paper Structure (8 sections, 246 equations)

This paper contains 8 sections, 246 equations.

Table of Contents

  1. Introduction
  2. Quantized enveloping algebras
  3. Quantized coordinate algebras
  4. Parabolic subalgebras
  5. Induction functor
  6. Equivariant modules
  7. Quantum groups of type $A$
  8. Main result

Theorems & Definitions (16)

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  • ...and 6 more