Попов Владимир Леонидович

The Jordan property for Lie groups and automorphism groups of complex spaces

2018 · PREPRINT · en

We prove that the family of all connected n-dimensional real Lie groups is uniformly Jordan for every n. This implies that all algebraic groups (not necessarily affine) over fields of cha\-racte\-ristic zero and some transformation groups of complex spaces and Riemannian manifods are Jordan.

The Jordan property for Lie groups and automorphism groups of complex spaces

2018 · ARTICLE · en

We prove that the family of all connected n-dimensional real Lie groups is uniformly Jordan for every n. This implies that all algebraic (not necessarily affine) groups over fields of characteristic zero and some transformation groups of complex spaces and Riemannian manifolds are Jordan.

Root systems in number fields

2018 · PREPRINT · en

We classify the types of root systems $R$ in the rings of integers of number fields $K$ such that the Weyl group $W(R)$ lies in the group $\mathcal L(K)$ generated by ${\rm Aut} (K)$ and multipli\-ca\-tions by the elements of $K^*$. We also classify the Weyl groups of roots systems of rank $n$ which are isomorphic to a subgroup of $\mathcal L(K)$ for a number field $K$ of degree $n$ over $\mathbb Q$.

Three plots about the Cremona groups

2018 в печати · PREPRINT · en

The first group of results of this paper concerns the compressibility of finite subgroups of the Cremona groups. The second concerns the embeddability of other groups in the Cremona groups and, conversely, the Cremona groups in other groups. The third concerns the connectedness of the Cremona groups.

Root symstems in number fields

2018 · PREPRINT · en

Lie Groups, Geometry, and Representation Theory. A Tribute to the Life and Work of Bertram Kostant

2018 · BOOK · en

This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 – February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant’s fundamental work in all of these areas has provided deep new insights and connections, and has created new fields of research. This volume features the only published articles of important recent results of the contributors with full details of their proofs. Key topics include: Poisson structures and potentials (A. Alekseev, A. Berenstein, B. Hoffman) Vertex algebras (T. Arakawa, K. Kawasetsu) Modular irreducible representations of semisimple Lie algebras (R. Bezrukavnikov, I. Losev) Asymptotic Hecke algebras (A. Braverman, D. Kazhdan) Tensor categories and quantum groups (A. Davydov, P. Etingof, D. Nikshych) Nil- Hecke algebras and Whittaker D-modules (V. Ginzburg) Toeplitz operators (V. Guillemin, A. Uribe, Z. Wang) Kashiwara crystals (A. Joseph) Characters of highest weight modules (V. Kac, M. Wakimoto) Alcove polytopes (T. Lam, A. Postnikov) Representation theory of quantized Gieseker varieties (I. Losev) Generalized Bruhat cells and integrable systems (J.-H. Liu, Y. Mi) Almost characters (G. Lusztig) Verlinde formulas (E. Meinrenken) Dirac operator and equivariant index (P.-É. Paradan, M. Vergne) Modality of representations and geometry of-groups (V. L. Popov) Distributions on homogeneous spaces (N. Ressayre) Reduction of orthogonal representations (J.- P. Serre).

Modality of representations and geometry of θ-groups

2018 · CHAPTER · en

We first establish several general properties of modality of algebraic group actions. In particular,we introduce the notion of a modality-regular action and prove that every visible action is modality-regular. Then, using these results, we classify irreducible linear representations of connected simple algebraic groups of every fixed modality to the case of any cyclically graded semisimple Lie algebra the notion of a packet (or a Jordan/decomposition class) and establish the properties of packets.

Compressible finite groups of birational automorphisms

2018 · ARTICLE · en

The compressibility of certain types of finite groups of birational automorphisms of algebraic varieties is established.

Types of root systems in number fields

2018 · ARTICLE · en

We classify the types of root systems R in the rings of integers of number fields K such that the Weyl group W(R) lies in the group generated by Aut(K) and multiplications by the elements of K*.

Do we create mathematics or do we gradually discover theories which exist somewhere independently of us?

2017 · ARTICLE · en

This is a preface to the paper A. Borel, "Mathematics: Art and Science" reprinted in EMS Newsletter, No. 103, March 2017.