53 citations · 507 across the 55 of their papers we have counts for
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Proof of the Knop conjecture
Ivan V. Losev
In this paper we prove the Knop conjecture asserting that two smooth affine spherical varieties with the same weight monoids are equivariantly isomorphic. We also state and prove a…
Computation of Weyl groups of G-varieties
Ivan V. Losev
Let G be a connected reductive group. To any irreducible G-variety one associates a certain linear group generated by reflections called the Weyl group. Weyl groups play an importa…
Embeddings of homogeneous spaces into irreducible modules
Ivan V. Losev
Let be a connected reductive group. We find a necessary and sufficient condition for a quasiaffine homogeneous space of to be embeddable into an irreducible -module. In…
Computation of the Cartan spaces of affine homogeneous spaces
Ivan V. Losev
Let be a reductive algebraic group and its reductive subgroup. Fix a Borel subgroup and a maximal torus . The Cartan space $\a_{G,G/H}$ is, by defi…
The Kempf-Ness theorem and Invariant Theory
Ivan V. Losev
We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.
Algebraic Hamiltonian actions
Ivan V. Losev
In this paper we deal with a Hamiltonian action of a reductive algebraic group on an irreducible normal affine Poisson variety . We study the invariant moment map $ψ_{G,X}:X…