174 citations · 376 across the 26 of their papers we have counts for
30 papers
On orthogonal projections related to representations of the Hecke algebra on a tensor space
Andrei Bytsko
We consider the problem of finding orthogonal projections of a rank that give rise to representations of the Hecke algebra in which the generators of the algebra a…
Two relations for the antisymmetrizer in the Hecke algebra
Andrei Bytsko
We prove two relations for the antisymmetrizer in the Hecke algebra and derive certain restrictions imposed by these relations on unitary representations of the Hecke algebra on te…
A relation for the Jones-Wenzl projector and tensor space representations of the Temperley-Lieb algebra
Andrei Bytsko
A relation for the Jones-Wenzl projector is proven. It has the following consequence for representations of the Temperley-Lieb algebra on tensor product spaces: if such a represent…
Totally positive matrices and dilogarithm identities
Andrei Bytsko, Alexander Volkov
We show that two involutions on the variety of upper triangular totally positive matrices are related, on the one hand, to the tetrahedron equation and, on the other hand,…
Tensor space representations of Temperley-Lieb algebra and generalized permutation matrices
Andrei Bytsko
Orthogonal projections in of rank one and rank two that give rise to unitary tensor space representations of the Temperley-Lieb algebra $TL_N(…
Tensor space representations of Temperley-Lieb algebra via orthogonal projections of rank
Andrei Bytsko
Unitary representations of the Temperley-Lieb algebra on the tensor space are considered. Two criteria are given for determining when an ort…