Speciality:
01.01.06 (Mathematical logic, algebra, and number theory)
Birth date:
4.02.1954
Website: https://im.bas-net.by/~suprunenko Keywords: representations of algebraic groups and finite groups îf Lie type; finite linear groups.
Subject:
The minimal polynomials of the images of unipotent elements in irreducible rational representations of the classical algebraic groups over fields of odd characteristic are found. For simple algebraic groups in positive characteristic $p$ a notion of a $p$-large representation is introduced and a number of propertiesof such representations of the classical algebraic groups isdescribed. Jointly with J. Brundan and A. S. Kleshchev a semisiplicity criterium for the restrictions of irreducible rational representations of the group $GL_n(K)$ in positive characteristic to a naturally embedded subgroup $GL_{n-1}(K)$ is established. Jointly with A. E. Zalesskii absolutely irreducible representations of finite groups of Lie type in defining characteristic containing matrices with simple spectra are described. Jointly with A. A. Baranov the branching rules for the modular fundamental representations of the symplectic groups are found and the minimal and minimal nontrivial inductive systems of irreducible representations of algebraic and locally finite groups of type $A_n$ are found.
Main publications:
Suprunenko I. D. On Jordan blocks of elements of order $p$ in irreducible representations of classical groups with $p$-large highest weights // J. Algebra. 1997, 191(2), 589–627.
Brundan J., Kleshchev A. S., and Suprunenko I. D. Semisimple restrictions from $GL(n)$ to $GL(n-1)$ // J. fuer die Reine und Ungew. Math. 1998, 500, 83–112.
Suprunenko I. D. and Zalesskii A. E. Irreducible representations of finite classical groups containing matrices with simple spectra // Commun. Algebra. 1998, 26(3), 863–888.
Suprunenko I. D. and Zalesskii A. E. Irreducible representations of finite exceptional groups of Lie type containing matrices with simple spectra // Commun. Algebra. 2000, 28(4), 1789–1833.
