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Nearby Cycle Sheaves for Symmetric Pairs

Mikhail Grinberg, Kari Vilonen, Ting Xue

Abstract

We present a nearby cycle sheaf construction in the context of symmetric spaces. This construction can be regarded as a replacement for the Grothendieck-Springer resolution in classical Springer theory.

Nearby Cycle Sheaves for Symmetric Pairs

Abstract

We present a nearby cycle sheaf construction in the context of symmetric spaces. This construction can be regarded as a replacement for the Grothendieck-Springer resolution in classical Springer theory.

Paper Structure

This paper contains 38 sections, 42 theorems, 301 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Symmetric pairs
  4. The little Weyl group Lg
  5. The equivariant fundamental group Lg
  6. The subgroups Lg and the concept of a regular splitting
  7. Statement of the main theorem
  8. Nearby cycle sheaves with twisted coefficients
  9. Monodromy in the family with twisted coefficients
  10. The group Lg and the Hecke algebra Lg
  11. A character of the component group Lg
  12. Statement of the theorem
  13. The Case Lg
  14. An example: the pair Lg
  15. Proofs of key preliminary results
  16. ...and 23 more sections

Key Result

Lemma 2.3

We have:

Theorems & Definitions (87)

  • Remark 2.1
  • Remark 2.2
  • Lemma 2.3
  • Remark 2.4
  • Definition 2.5
  • Proposition 2.6
  • Lemma 2.7
  • Proposition 3.1
  • Corollary 3.2
  • proof
  • ...and 77 more