representations of algebraic groups and finite groups оf 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.
Biography
Graduated from the Mechanics and Mathematics Department of the Belarus State University in 1976 (the Higher Algebra Chair). Ph.D., 1979, the Institute of Mathematics, the National Academy of Sciences of Belarus. Doct. Sci., 1997, the same institute. More than 80 publications.
A member of the Belarus and American Mathematical Societies.
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.
T. S. Busel, I. D. Suprunenko, “Блочная структура образов регулярных унипотентных элементов из подсистемных симплектических подгрупп ранга 2 в неприводимых представлениях симплектических групп. III”, Mat. Tr., 23:2 (2020), 70–99
2.
T. S. Busel, I. D. Suprunenko, “Блочная структура образов регулярных унипотентных элементов из подсистемных симплектических подгрупп ранга $2$ в неприводимых представлениях симплектических групп. II”, Mat. Tr., 23:1 (2020), 37–106
3.
T. S. Busel, I. D. Suprunenko, “On the properties of irreducible representations of special linear and symplectic groups that are not large with respect to the field characteristic and regular unipotent elements from subsystem subgroups”, Trudy Inst. Mat. i Mekh. UrO RAN, 26:2 (2020), 88–97
2019
4.
T. S. Busel, I. D. Suprunenko, “Блочная структура образов регулярных унипотентных элементов из подсистемных симплектических подгрупп ранга $2$ в неприводимых представлениях симплектических групп. I”, Mat. Tr., 22:1 (2019), 68–100
2018
5.
N. A. Izobov, V. V. Gorokhovik, Yu. S. Kharin, L. A. Yanovich, D. F. Bazylev, V. V. Benyash-Krivets, I. D. Suprunenko, S. V. Tikhonov, “V. I . Yanchevskii is 70”, Algebra Discrete Math., 26:1 (2018), C–F
2015
6.
I. D. Suprunenko, “Big composition factors in restrictions of representations of the special linear group to subsystem subgroups with two simple components”, Tr. Inst. Mat., 23:2 (2015), 123–136
2014
7.
A. A. Osinovskaya, I. D. Suprunenko, “Inductive systems of representations with small highest weights for natural embeddings of symplectic groups”, Tr. Inst. Mat., 22:2 (2014), 109–118
2013
8.
A. S. Kondrat'ev, A. A. Osinovskaya, I. D. Suprunenko, “On the behavior of elements of prime order from a Zinger cycle in representations of a special linear group”, Trudy Inst. Mat. i Mekh. UrO RAN, 19:3 (2013), 179–186; Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), S108–S115
9.
I. D. Suprunenko, “Unipotent elements of nonprime order in representations of the classical algebraic groups: two big Jordan blocks”, Zap. Nauchn. Sem. POMI, 414 (2013), 193–241; J. Math. Sci. (N. Y.), 199:3 (2014), 350–374
2011
10.
I. D. Suprunenko, “On the block structure of regular unipotent elements from subsystem subgroups of type $A_1\times A_2$ in representations of the special linear group”, Zap. Nauchn. Sem. POMI, 388 (2011), 247–269; J. Math. Sci. (N. Y.), 183:5 (2012), 715–726
2010
11.
A. A. Osinovskaya, I. D. Suprunenko, “Representations of algebraic groups of type $C_n$ with small weight multiplicities”, Zap. Nauchn. Sem. POMI, 375 (2010), 140–166; J. Math. Sci. (N. Y.), 171:3 (2010), 386–399
2009
12.
A. A. Osinovskaya, I. D. Suprunenko, “Representations of algebraic groups of type $D_n$ in characteristic 2 with small weight multiplicities”, Zap. Nauchn. Sem. POMI, 365 (2009), 182–195; J. Math. Sci. (N. Y.), 161:4 (2009), 558–564
2007
13.
M. V. Velichko, A. A. Osinovskaya, I. D. Suprunenko, “The group generated by round permutations of the cryptosystem BelT”, Tr. Inst. Mat., 15:1 (2007), 15–21
14.
M. V. Velichko, I. D. Suprunenko, “On the behaviour of small quadratic elements in representations of the special linear group with large highest weights”, Zap. Nauchn. Sem. POMI, 343 (2007), 84–120; J. Math. Sci. (N. Y.), 147:5 (2007), 7021–7041
1996
15.
I. D. Suprunenko, “Minimal polynomials of elements of order $p$ in irreducible representations of Chevalley groups over fields of characteristic $p$”, Trudy Inst. Mat. SO RAN, 30 (1996), 126–163
1990
16.
A. E. Zalesskii, I. D. Suprunenko, “Permutation representations and a fragment of the decomposition matrix of symplectic and special linear groups over a finite field”, Sibirsk. Mat. Zh., 31:5 (1990), 46–60; Siberian Math. J., 31:5 (1990), 744–755
17.
A. E. Zalesskii, I. D. Suprunenko, “Truncated symmetric powers of natural realizations of the groups $SL_m(P)$ and $Sp_m(P)$ and their constraints on subgroups”, Sibirsk. Mat. Zh., 31:4 (1990), 33–46; Siberian Math. J., 31:4 (1990), 555–566
1979
18.
I. D. Suprunenko, “Subgroups of $G(n,p)$ containing $SL(2,p)$ in an irreducible representation of degree $n$”, Mat. Sb. (N.S.), 109(151):3(7) (1979), 453–468; Math. USSR-Sb., 37:3 (1980), 425–440
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