Categorification of tensor powers of the vector representation of $U_q(\mathfrak{gl}(1|1))$

Antonio Sartori

Categorification of tensor powers of the vector representation of $U_q(\mathfrak{gl}(1|1))$

Representation Theory 2015-01-12 v3 Quantum Algebra

Authors: Antonio Sartori

Abstract

We consider the monoidal subcategory of finite dimensional representations of $U_q(\mathfrak{gl}(1|1))$ generated by the vector representation, and we provide a diagram calculus for the intertwining operators, which allows to compute explicitly the canonical basis. We construct then a categorification of these representations and of the action of both $U_q(\mathfrak{gl}(1|1))$ and the intertwining operators using subquotient categories of the BGG category $\mathcal{O}(\mathfrak{gl}_n)$ .

Keywords

categorification tensor powers vector representation $U_q(\mathfrak{gl}(1|1))$ diagram calculus canonical basis BGG category $\mathcal{O}$

Cite

@article{arxiv.1305.6162,
  title  = {Categorification of tensor powers of the vector representation of $U_q(\mathfrak{gl}(1|1))$},
  author = {Antonio Sartori},
  journal= {arXiv preprint arXiv:1305.6162},
  year   = {2015}
}

Comments

This is a revised version, with many corrections and improvements. This article is part of the author's PhD thesis

Categorification of tensor powers of the vector representation of $U_q(\mathfrak{gl}(1|1))$

Abstract

Keywords

Cite

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