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, “The Jordan block structure of the images of unipotent elements in irreducible modular representations of classical algebraic groups of small dimensions”, Sib. Èlektron. Mat. Izv., 20:1 (2023), 306–454
2.
I. D. Suprunenko, T. S. Busel, A. A. Osinovskaya, “Special factors in the restrictions of irreducible modules of classical groups to subsystem subgroups with two simple components”, Trudy Inst. Mat. i Mekh. UrO RAN, 29:4 (2023), 259–273
2022
3.
T. S. Busel, I. D. Suprunenko, “On the behaviour of unipotent elements from subsystem subgroups of small ranks in irreducible representations of the classical algebraic groups in positive characteristic”, Tr. Inst. Mat., 30:1-2 (2022), 117–129
4.
A. S. Kondrat'ev, I. D. Suprunenko, I. V. Khramtsov, “On finite 4-primary groups having a disconnected Gruenberg-Kegel graph and a composition factor isomorphic to $L_3(17)$ or $Sp_4(4)$”, Trudy Inst. Mat. i Mekh. UrO RAN, 28:1 (2022), 139–155
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
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
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
8.
T. S. Busel, I. D. Suprunenko, “The block structure of the images of regular unipotent elements from subsystem symplectic subgroups of rank $2$ in irreducible representations of symplectic groups. I”, Mat. Tr., 22:1 (2019), 68–100; Siberian Adv. Math., 30:1 (2020), 1–20
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
10.
I. D. Suprunenko, “Special composition factors in restrictions of representations of special linear andsymplectic groups to subsystem subgroups with two simple components”, Tr. Inst. Mat., 26:1 (2018), 113–133
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
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
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
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
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
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
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
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
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
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
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
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
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
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, “Member of the National Academy of Sciences of Belarus V.I. Yanchevskii. Towards the 70th birthday”, Tr. Inst. Mat., 26:1 (2018), 6–8
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