M. V. Ignat'ev, “Orthogonal Subsets of Classical Root Systems and Coadjoint Orbits of Unipotent Groups”, Mat. Zametki, 86:1 (2009), 65–80; Math. Notes, 86:1 (2009), 65

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Matematicheskie Zametki, 2009, Volume 86, Issue 1, Pages 65–80
DOI: https://doi.org/10.4213/mzm6356 (Mi mzm6356)

This article is cited in 10 scientific papers (total in 10 papers)

Orthogonal Subsets of Classical Root Systems and Coadjoint Orbits of Unipotent Groups

M. V. Ignat'ev

Samara State University

Full-text PDF (558 kB) Citations (10)

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DOI: https://doi.org/10.4213/mzm6356

Abstract: We consider a specific class of coadjoint orbits of maximal unipotent subgroups in classical groups over a finite field, i.e., orbits associated with orthogonal subsets in root systems. We derive a formula for the dimension of these orbits in terms of the Weyl group and construct polarizations for canonical forms on the orbits. As a consequence, we describe all possible dimensions of irreducible representations of such unipotent groups.

Keywords: root system, coadjoint orbits, unipotent group, polarization, Weyl group, irreducible representation, irreducible complex character, polarization of linear forms.

Received: 20.10.2008

English version:
Mathematical Notes, 2009, Volume 86, Issue 1, Pages 65–80
DOI: https://doi.org/10.1134/S0001434609070074

Bibliographic databases:

UDC: 512.547.214+512.743.7

Language: Russian

Citation: M. V. Ignat'ev, “Orthogonal Subsets of Classical Root Systems and Coadjoint Orbits of Unipotent Groups”, Mat. Zametki, 86:1 (2009), 65–80; Math. Notes, 86:1 (2009), 65–80

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm6356

https://doi.org/10.4213/mzm6356

https://www.mathnet.ru/eng/mzm/v86/i1/p65

This publication is cited in the following 10 articles:

Mikhail V. Ignatev, “Gradedness of the set of rook placements in A
n-1”, Communications in Mathematics, 29:2 (2021), 171
Ignatyev M.V., “Centrally Generated Primitive Ideals of U(N) in Types B and D”, Transform. Groups, 24:4 (2019), 1067–1093
Mikhail V. Ignatyev, Progress in Mathematics, 330, Representations and Nilpotent Orbits of Lie Algebraic Systems, 2019, 331
Ignatyev M.V., Penkov I., “Infinite Kostant cascades and centrally generated primitive ideals of $U(\mathfrak n)$ in types $A_{\infty}, C_{\infty}$ ”, J. Algebra, 447 (2016), 109–134
Bochkarev M.A., Ignatyev M.V., Shevchenko A.A., “Tangent cones to Schubert varieties in types An, Bn and Cn”, J. Algebra, 465 (2016), 259–286
M. V. Ignatyev, A. A. Shevchenko, “On tangent cones to Schubert varieties in type $D_n$ ”, St. Petersburg Math. J., 27:4 (2016), 609–623
M. V. Ignatyev, A. S. Vasyukhin, “Rook placements in $a_N$ and combinatorics of $B$ -orbit closures”, J. Lie Theory, 24:4 (2014), 931–956
Ignatyev M.V., “Combinatorics of $B$ -orbits and Bruhat-Chevalley order on involutions”, Transform. Groups, 17:3 (2012), 747–780
M. V. Ignat'ev, “The Bruhat–Chevalley order on involutions of the hyperoctahedral group and combinatorics of $B$ -orbit closures”, J. Math. Sci. (N. Y.), 192:2 (2013), 220–231
M. V. Ignat'ev, “Orthogonal subsets of root systems and the orbit method”, St. Petersburg Math. J., 22:5 (2011), 777–794

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Full-text PDF :	224
References:	67
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