12 citations · 27 across the 16 of their papers we have counts for
22 papers
On fusion product and N!/k-conjecture
Anton Khoroshkin, Ievgen Makedonskyi
We formulate a version of Schur--Weyl duality for the current Lie algebra . Under this duality, the Garsia--Haiman modul…
Categorification of the genus two DAHA
Semeon Arthamonov, Ievgen Makedonskyi, Daniil Sarafannikov
We construct three derived endofunctors on the derived category of graded integrable representations of the current algebra of a flat degeneration of , and prove that the…
Bubble sort and Howe duality for staircase matrices
Anton Khoroshkin, Ievgen Makedonskyi
We prove the alternating Cauchy identity for staircase matrices conjectured in arXiv:2411.03117, together with an explicit description of the coefficients occurring in it. As a byp…
Cauchy identities for staircase matrices
Evgeny Feigin, Anton Khoroshkin, Ievgen Makedonskyi
The well known Cauchy identity expresses the product of terms for indexing entries of a rectangular -matrix as a sum over partitions of…
Poset polytopes and pipe dreams: toric degenerations and beyond
Ievgen Makedonskyi, Igor Makhlin
We demonstrate how pipe dreams can be applied to the theory of poset polytopes to produce toric degenerations of flag varieties. Specifically, we present such constructions for mar…
Poset polytopes and pipe dreams: types C and B
Ievgen Makedonskyi, Igor Makhlin
The first part of this paper concerns type C. We present new explicitly defined families of algebro-combinatorial structures of three kinds: combinatorial bases in representations,…
Parahoric Lie algebras and parasymmetric Macdonald polynomials
Evgeny Feigin, Anton Khoroshkin, Ievgen Makedonskyi
The main goal of this paper is to categorify the specialized parasymmetric (intermediate) Macdonald polynomials. These polynomials depend on a parabolic subalgebra of a simple Lie…
Peter-Weyl theorem for Iwahori groups and highest weight categories
Evgeny Feigin, Anton Khoroshkin, Ievgen Makedonskyi +1
We study the algebra of functions on the Iwahori group via the category of graded bounded representations of its Lie algebra. In particular, we identify the standard and costandard…
Nonsymmetric -Cauchy identity and representations of the Iwahori algebra
Evgeny Feigin, Ievgen Makedonskyi, Daniel Orr
The specialization of the Mimachi-Noumi Cauchy-type identity rewrites certain infinite product in terms of specialized nonsymmetric Macdonald polynomials of type . We i…
On reduced arc spaces of toric varieties
Ilya Dumanski, Evgeny Feigin, Ievgen Makedonskyi +1
An arc space of an affine cone over a projective toric variety is known to be non-reduced in general. It was demonstrated recently that the reduced scheme structure is worth studyi…
Categorification of DAHA and Macdonald polynomials
Syu Kato, Anton Khoroshkin, Ievgen Makedonskyi
We describe a categorification of the Double Affine Hecke Algebra () associated with an affine Lie algebra , including…
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…
Semi-infinite Plücker relations and Weyl modules
Evgeny Feigin, Ievgen Makedonskyi
The goal of this paper is twofold. First, we write down the semi-infinite Plücker relations, describing the Drinfeld-Plücker embedding of the (formal version of) semi-infinite flag…
Representation theoretic realization of non-symmetric Macdonald polynomials at infinity
Evgeny Feigin, Syu Kato, Ievgen Makedonskyi
We study the nonsymmetric Macdonald polynomials specialized at infinity from various points of view. First, we define a family of modules of the Iwahori algebra whose characters ar…
Generalized Weyl modules for twisted current algebras
Evgeny Feigin, Ievgen Makedonskyi
We introduce the notion of generalized Weyl modules for twisted current algebras. We study their representation-theoretic and combinatorial properties and connection to the theory…
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…
Generalized Weyl modules, alcove paths and Macdonald polynomials
Evgeny Feigin, Ievgen Makedonskyi
Classical local Weyl modules for a simple Lie algebra are labeled by dominant weights. We generalize the definition to the case of arbitrary weights and study the properties of the…
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…
Nonsymmetric Macdonald polynomials, Demazure modules and PBW filtration
Evgeny Feigin, Ievgen Makedonskyi
The Cherednik-Orr conjecture expresses the limit of the nonsymmetric Macdonald polynomials in terms of the PBW twisted characters of the affine level one Demazure modu…
On wild Lie algebras
Ievgen Makedonskyi
We give a criterion of tameness and wildness for a finite-dimensional Lie algebra over an algebraically closed field.