UNIVERSAL FORMULA FOR THE HILBERT SERIES OF MINIMAL NILPOTENT ORBITS

被引：2

作者：

Matsuo, A. ^{[1
]}

Veselov, A. P. ^{[2
,3
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Tokyo 1538914, Japan

[2] Loughborough Univ Technol, Dept Math Sci, Loughborough LE11 3TU, Leics, England

[3] Moscow MV Lomonosov State Univ, Moscow 119899, Russia

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 145卷 / 12期

关键词：

DIMENSION; IDEAL;

D O I：

10.1090/proc/13819

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the Hilbert series of the projective variety X = P(O-min), corresponding to the minimal nilpotent orbit O-min, is universal in the sense of Vogel: it is written uniformly for all simple Lie algebras in terms of Vogel's parameters alpha, beta, gamma and represents a special case of the generalized hypergeometric function F-4(3). A universal formula for the degree of X is then deduced.

引用

页码：5123 / 5130

页数：8

共 50 条

[1] Series of nilpotent orbits
Landsberg, JM
Manivel, L
Westbury, BW
[J]. EXPERIMENTAL MATHEMATICS, 2004, 13 (01) : 13 - 29
[2] A limit formula for even nilpotent orbits
Bozicevic, Mladen
[J]. INTERNATIONAL JOURNAL OF MATHEMATICS, 2008, 19 (02) : 223 - 236
[3] Springer Fibers for the Minimal and the Minimal Special Nilpotent Orbits
Kim, Dongkwan
[J]. ALGEBRAS AND REPRESENTATION THEORY, 2019, 22 (03) : 545 - 567
[4] Springer Fibers for the Minimal and the Minimal Special Nilpotent Orbits
Dongkwan Kim
[J]. Algebras and Representation Theory, 2019, 22 : 545 - 567
[5] Geometric quantization of real minimal nilpotent orbits
Brylinski, R
[J]. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 1998, 9 (1-2) : 5 - 58
[6] EQUIVARIANT HILBERT SERIES OF MONOMIAL ORBITS
Gunturkun, Sema
Nagel, Uwe
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146 (06) : 2381 - 2393
[7] Universal denominators of Hilbert series
Derksen, H
[J]. JOURNAL OF ALGEBRA, 2005, 285 (02) : 586 - 607
[8] NILPOTENT SUBSPACES AND NILPOTENT ORBITS
Panyushev, Dmitri, I
Yakimova, Oksana S.
[J]. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2019, 106 (01) : 104 - 126
[9] INVARIANT MEASURES ON NILPOTENT ORBITS ASSOCIATED WITH HOLOMORPHIC DISCRETE SERIES
Bozicevic, Mladen
[J]. REPRESENTATION THEORY, 2021, 25 : 732 - 747
[10] ALMOST EVERY QUASI-NILPOTENT HILBERT-SPACE OPERATOR IS A UNIVERSAL QUASI-NILPOTENT
HERRERO, DA
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1978, 71 (02) : 212 - 216

← 1 2 3 4 5 →