Abstract
We show that the Duflo–Serganova functor on the category of finite-dimensional modules over a finite-dimensional contragredient Lie superalgebra induces a ring homomorphism on a natural quotient of the Grothendieck ring, which is isomorphic to the ring of supercharacters. We realize this homomorphism as a certain evaluation of functions related to the supersymmetry property. We use this realization to describe the kernel and image of the homomorphism induced by the Duflo–Serganova functor.
| Original language | English |
|---|---|
| Pages (from-to) | 2167-2184 |
| Number of pages | 18 |
| Journal | Algebra and Number Theory |
| Volume | 12 |
| Issue number | 9 |
| DOIs | |
| State | Published - 2018 |
Bibliographical note
Publisher Copyright:© 2018, Mathematical Sciences Publishers. All rights reserved.
Funding
Hoyt was partially supported by BSF Grant 2012227. Reif was partially supported by ORT Braude College’s Research Authority. MSC2010: primary 17B10; secondary 05E05, 05E10. Keywords: Lie superalgebra, supercharacter, Grothendieck ring, Duflo–Serganova functor, supersymmetric Laurent polynomials.
| Funders | Funder number |
|---|---|
| ORT Braude College’s Research Authority | |
| United States-Israel Binational Science Foundation | 2012227 |
Keywords
- Duflo-Serganova functor
- Grothendieck ring
- Lie superalgebra
- Supercharacter
- Supersymmetric Laurent polynomials