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18 papers · 1 filter
Standard Lyndon loop words: weighted orders
Severyn Khomych, Nazar Korniichuk, Kostiantyn Molokanov +1
We generalize the study of standard Lyndon loop words from [A.Negut, A.Tsymbaliuk, "Quantum loop groups and shuffle algebras via Lyndon words", Adv. Math. 439 (2024), Paper No. 109…
Unitarity of minimal -algebras and their representations II: Ramond sector
Victor G. Kac, Pierluigi Möseneder Frajria, Paolo Papi
In this paper we study unitary Ramond twisted representations of minimal -algebras. We classify all such irreducible highest weight representations with a non-Ramond extremal hi…
On a symplectic quantum Howe duality
Elijah Bodish, Daniel Tubbenhauer
We prove a nonsemisimple quantum version of Howe's duality with the rank 2n symplectic and the rank 2 special linear group acting on the exterior algebra of type C. We also discuss…
Unitarity of minimal -algebras and their representations I
Victor G. Kac, Pierluigi Möseneder Frajria, Paolo Papi
We begin a systematic study of unitary representations of minimal -algebras. In particular, we classify unitary minimal -algebras and make substantial progress in classificat…
Modular affine Hecke category and regular centralizer
Roman Bezrukavnikov, Simon Riche
In this paper we provide a "combinatorial" description of the category of tilting perverse sheaves on the affine flag variety of a reductive algebraic group, and its free-monodromi…
Transfer matrices of rational spin chains via novel BGG-type resolutions
Rouven Frassek, Ivan Karpov, Alexander Tsymbaliuk
We obtain BGG-type formulas for transfer matrices of irreducible finite-dimensional representations of the classical Lie algebras , whose highest weight is a multiple…