We compute dimensions of the components for the operad of two compatible brackets and for the bihamiltonian operad. We also obtain character formulas for the representations of the symmetric groupsâ€¦ (More)

We prove the conjectures on dimensions and characters of some quadratic algebras stated by B.L.Feigin. It turns out that these algebras are naturally isomorphic to the duals of the components of theâ€¦ (More)

Using the approach suggested in [2] we present below a sufficient condition guaranteeing that two collections of patterns of permutations have the same exponential generating functions for the numberâ€¦ (More)

The main goal of this paper is to present a way to compute Quillen homology of operads. The key idea is to use the notion of a shuffle operad we introduced earlier; this allows to compute, for aâ€¦ (More)

We consider the graded space R of syzygies for the coordinate algebra A of projective variety X = G/P embedded into projective space as an orbit of the highest weight vector of an irreducibleâ€¦ (More)

We study the category Igr of graded representations with finite-dimensional graded pieces for the current algebra g âŠ— C[t] where g is a simple Lie algebra. This category has many similarities withâ€¦ (More)