7 papers
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…
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…
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…
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,…
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…
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…