15 citations · 86 across the 13 of their papers we have counts for
13 papers
Root subgroups on affine spherical varieties
Ivan Arzhantsev, Roman Avdeev
Given a connected reductive algebraic group and a Borel subgroup , we study -normalized one-parameter additive group actions on affine spherical -varieties…
On extended weight monoids of spherical homogeneous spaces
Roman Avdeev
Given a connected reductive complex algebraic group and a spherical subgroup , the extended weight monoid encodes the -module structures o…
Degenerations of spherical subalgebras and spherical roots
Roman Avdeev
We obtain several structure results for a class of spherical subgroups of connected reductive complex algebraic groups that extends the class of strongly solvable spherical subgrou…
Spherical actions on isotropic flag varieties and related branching rules
Roman Avdeev, Alexey Petukhov
Let be a symplectic or special orthogonal group, let be a connected reductive subgroup of , and let be a flag variety of . We classify all triples such…
Branching rules related to spherical actions on flag varieties
Roman Avdeev, Alexey Petukhov
Let be a connected semisimple algebraic group and let be a connected reductive subgroup. Given a flag variety of , a result of Vinberg and Kimelfeld assert…
New and old results on spherical varieties via moduli theory
Roman Avdeev, Stéphanie Cupit-Foutou
Given a connected reductive algebraic group and a finitely generated monoid of dominant weights of , in 2005 Alexeev and Brion constructed a moduli scheme …
On the irreducible components of moduli schemes for affine spherical varieties
Roman Avdeev, Stéphanie Cupit-Foutou
We give a combinatorial description of all affine spherical varieties with prescribed weight monoid . As an application, we obtain a characterization of the irreducible componen…
Strongly solvable spherical subgroups and their combinatorial invariants
Roman Avdeev
A subgroup H of an algebraic group G is said to be strongly solvable if H is contained in a Borel subgroup of G. This paper is devoted to establishing relationships between the fol…
Normalizers of solvable spherical subgroups
Roman Avdeev
For an arbitrary connected solvable spherical subgroup H of a connected semisimple algebraic group G we compute the group N_G(H), the normalizer of H in G. Thereby we complete a cl…
Affine spherical homogeneous spaces with good quotient by a maximal unipotent subgroup
Roman Avdeev
For an affine spherical homogeneous space G/H of a connected semisimple algebraic group G, we consider the factorization morphism by the action on G/H of a maximal unipotent subgro…
On solvable spherical subgroups of semisimple algebraic groups
Roman Avdeev
We develop a structure theory of connected solvable spherical subgroups in semisimple algebraic groups. Based on this theory, we obtain an explicit classification of all such subgr…
An epimorphic subgroup arising from Roberts' counterexample
Roman Avdeev
In 1994, based on Roberts' counterexample to Hilbert's fourteenth problem, A'Campo-Neuen constructed an example of a linear action of a 12-dimensional commutative unipotent group H…
Extended weight semigroups of affine spherical homogeneous spaces of non-simple semisimple algebraic groups
Roman Avdeev
The extended weight semigroup of a homogeneous space G/H of a connected semisimple algebraic group G characterizes the spectra of the representations of G on the spaces of regular…