53 citations · 507 across the 55 of their papers we have counts for
6 papers · 2 filters
Representations of general linear groups and categorical actions of Kac-Moody algebras
Ivan Losev
This is an expanded version of the lectures given by the author on the 3rd school "Lie algebras, algebraic groups and invariant theory" in Togliatti, Russia. In these notes we expl…
Dimensions of irreducible modules over W-algebras and Goldie ranks
Ivan Losev
The main goal of this paper is to compute two related numerical invariants of a primitive ideal in the universal enveloping algebra of a semisimple Lie algebra. The first one, very…
Towards multiplicities for categories O of cyclotomic rational Cherednik algebras
Ivan Losev
Varagnolo and Vasserot conjectured an equivalence between the category O for a cyclotomic Rational Cherednik algebra and a truncation of an affine parabolic category O of type A. I…
Highest weight sl_2-categorifications II: structure theory
Ivan Losev
This paper continues the study of highest weight categorical sl_2-actions started in part I. We start by refining the definition given there and showing that all examples considere…
Highest weight sl_2-categorifications I: crystals
Ivan Losev
We define highest weight categorical actions of sl_2 on highest weight categories and show that basically all known examples of categorical sl_2-actions on highest weight categorie…
Classification of finite dimensional irreducible modules over W-algebras
Ivan Losev, Victor Ostrik
Finite W-algebras are certain associative algebras arising in Lie theory. Each W-algebra is constructed from a pair of a semisimple Lie algebra g (our base field is algebraically c…