RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find

 Izv. Akad. Nauk SSSR Ser. Mat., 1982, Volume 46, Issue 2, Pages 347–370 (Mi izv1619)

A finiteness theorem for representations with a free algebra of invariants

V. L. Popov

Abstract: It is proved that for any connected semisimple algebraic group $G$ defined over an algebraically closed field of characteristic zero there exist (up to isomorphism) only a finite number of finite-dimensional rational $G$-modules containing no nonzero fixed vectors and having a free algebra of invariants. The proof is constructive and makes it possible in principle to indicate these $G$-modules explicitly. It is also proved that for all irreducible $G$-modules $V$, except for a finite number, the degree of the Poincaré series of the algebra of invariants (regarded as a rational function) equals $-\dim V$.
Bibliography: 21 titles.

Full text: PDF file (2426 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1983, 20:2, 333–354

Bibliographic databases:

UDC: 519.4
MSC: Primary 15A72, 20G05; Secondary 52A25

Citation: V. L. Popov, “A finiteness theorem for representations with a free algebra of invariants”, Izv. Akad. Nauk SSSR Ser. Mat., 46:2 (1982), 347–370; Math. USSR-Izv., 20:2 (1983), 333–354

Citation in format AMSBIB
\Bibitem{Pop82} \by V.~L.~Popov \paper A~finiteness theorem for representations with a~free algebra of invariants \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1982 \vol 46 \issue 2 \pages 347--370 \mathnet{http://mi.mathnet.ru/izv1619} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=651651} \zmath{https://zbmath.org/?q=an:0547.20034} \transl \jour Math. USSR-Izv. \yr 1983 \vol 20 \issue 2 \pages 333--354 \crossref{https://doi.org/10.1070/IM1983v020n02ABEH001353} 

• http://mi.mathnet.ru/eng/izv1619
• http://mi.mathnet.ru/eng/izv/v46/i2/p347

 SHARE:

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

This publication is cited in the following articles:
1. V. L. Popov, “Syzygies in the theory of invariants”, Math. USSR-Izv., 22:3 (1984), 507–585
2. D. I. Panyushev, “Regular elements in spaces of linear representations of reductive algebraic groups”, Math. USSR-Izv., 24:2 (1985), 383–390
3. N Alon, K.A Berman, “Regular hypergraphs, Gordon's lemma, Steinitz' lemma and invariant theory”, Journal of Combinatorial Theory, Series A, 43:1 (1986), 91
4. D. I. Panyushev, “Orbits of maximal dimension of solvable subgroups of reductive linear groups, and reduction for $U$-invariants”, Math. USSR-Sb., 60:2 (1988), 365–375
•  Number of views: This page: 286 Full text: 79 References: 60 First page: 4