An equivalence of two categories of sl(n, C)-modules

An equivalence of two categories of sl(n,C)-modules

Twisted Sheaves on Flag Varieties: sl(2,C) Calculations

These are notes from a series of talks given in the representation theory student seminar at the University of Utah in November 2016. These talks explored the twists that arise in the geometry of the Borel Weil theorem and Beilinson and Bernstein’s equivalence of categories. Throughout the talks, we assume g = sl(2,C). We discuss the Serre’s twisted sheaves of sections of line bundles, sheaves ...

Modules of the toroidal Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$

‎Highest weight modules of the double affine Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎Singular vectors of Verma modules are‎ ‎determined using a similar condition with horizontal affine Lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

On the Structure of the Fundamental Series of Generalized Harish-chandra Modules

We continue the study of the fundamental series of generalized Harish-Chandra modules initiated in [PZ2]. Generalized Harish-Chandra modules are (g, k)-modules of finite type where g is a semisimple Lie algebra and k ⊂ g is a reductive in g subalgebra. A first result of the present paper is that a fundamental series module is a g-module of finite length. We then define the notions of strongly a...

Equivalences in Bicategories

In this paper, we establish some connections between the concept of an equivalence of categories and that of an equivalence in a bicategory. Its main result builds upon the observation that two closely related concepts, which could both play the role of an equivalence in a bicategory, turn out not to coincide. Two counterexamples are provided for that goal, and detailed proofs are given. In par...