2 citations · 3 across the 3 of their papers we have counts for
5 papers
Semi-infinite Plücker relations and arcs over toric degeneration
Ievgen Makedonskyi
We study the algebra of Weyl modules in types and using the methods of arcs over toric degenerations and functional realization of dual space. We compute the generators and…
Peter-Weyl, Howe and Schur-Weyl theorems for current groups
Evgeny Feigin, Anton Khoroshkin, Ievgen Makedonskyi
The classical Peter-Weyl theorem describes the structure of the space of functions on a semi-simple algebraic group. On the level of characters (in type A) this boils down to the C…
Vertex algebras and coordinate rings of semi-infinite flags
Evgeny Feigin, Ievgen Makedonskyi
The direct sum of irreducible level one integrable representations of affine Kac-Moody Lie algebra of (affine) type carries a structure of -graded vertex operator algebr…
Generalized Weyl modules and nonsymmetric -Whittaker functions
Evgeny Feigin, Ievgen Makedonskyi, Daniel Orr
We introduce generalized global Weyl modules and relate their graded characters to nonsymmetric Macdonald polynomials and nonsymmetric -Whittaker functions. In particular, we sh…
Weyl modules for and nonsymmetric Macdonald polynomials
Evgeny Feigin, Ievgen Makedonskyi
The main goal of our paper is to establish a connection between the Weyl modules of the current Lie superalgebras (twisted and untwisted) attached to and the…