Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

p-DG cyclotomic nilHecke algebras

Mikhail Khovanov, You Qi, Joshua Sussan

Abstract

We categorify a tensor product of two Weyl modules for quantum sl(2) at a prime root of unity.

p-DG cyclotomic nilHecke algebras

Abstract

We categorify a tensor product of two Weyl modules for quantum sl(2) at a prime root of unity.

Paper Structure

This paper contains 49 sections, 73 theorems, 418 equations.

Table of Contents

  1. Introduction
  2. Motivation
  3. Summary of contents
  4. Further comments
  5. Acknowledgements.
  6. The quantum group at prime roots of unity
  7. The small quantum sl(2)
  8. The BLM integral form
  9. Representations
  10. Elements of hopfological algebra
  11. p-DG derived categories
  12. Hopfological properties of p-DG modules
  13. p-DG functors
  14. Grothendieck groups
  15. A double centralizer property
  16. ...and 34 more sections

Key Result

Theorem 1

There is an action of the derived $p$-DG Lauda category on $\oplus_{n=0}^l \mathcal{D}(S_n(r,s))$. The action induces an identification of the Grothendieck groups with the tensor product of the quantum $\mathfrak{sl}_2$ Weyl modules $V_r$ and $V_s$ at a primitive $p$th root of unity.

Theorems & Definitions (215)

  • Theorem : \ref{['mainthm']}
  • Definition 2.1
  • Definition 2.2
  • Proposition 2.3
  • proof
  • Remark 2.4
  • Definition 3.1
  • Definition 3.2
  • Definition 3.3
  • Definition 3.4
  • ...and 205 more