A cubic Dirac operator and the emergence of Euler number multiplets of representations for equal rank subgroups
Bertram Kostant
Source: Duke Math. J. Volume 100, Number 3
(1999), 447-501.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077227495
Mathematical Reviews number (MathSciNet): MR1719734
Zentralblatt MATH identifier: 0952.17005
Digital Object Identifier: doi:10.1215/S0012-7094-99-10016-0
References
[AM] A. Alekseev and E. Meinreinken, Noncommutative Weil algebra, preprint.
[Ch1] Claude C. Chevalley, The algebraic theory of spinors, Columbia University Press, New York, 1954.
Mathematical Reviews (MathSciNet): MR15,678d
Zentralblatt MATH: 0057.25901
[Ch2] Claude Chevalley, Invariants of finite groups generated by reflections, Amer. J. Math. 77 (1955), 778–782.
Mathematical Reviews (MathSciNet): MR17,345d
Zentralblatt MATH: 0065.26103
Digital Object Identifier: doi:10.2307/2372597
JSTOR: links.jstor.org
[CG] Neil Chriss and Victor Ginzburg, Representation theory and complex geometry, Birkhäuser Boston Inc., Boston, MA, 1997.
Mathematical Reviews (MathSciNet): MR98i:22021
Zentralblatt MATH: 0879.22001
[Co] Lawrence Conlon, A class of variationally complete representations, J. Differential Geometry 7 (1972), 149–160.
Mathematical Reviews (MathSciNet): MR51:14123
Zentralblatt MATH: 0276.53038
Project Euclid: euclid.jdg/1214430824
[FdV] Hans Freudenthal and H. de Vries, Linear Lie groups, Pure and Applied Mathematics, Vol. 35, Academic Press, New York, 1969.
Mathematical Reviews (MathSciNet): MR41:5546
Zentralblatt MATH: 0377.22001
[GHV] Werner Greub, Stephen Halperin, and Ray Vanstone, Connections, curvature, and cohomology. Vol. I: De Rham cohomology of manifolds and vector bundles, Pure Appl. Math., vol. 47-III, Academic Press, New York, 1972.
Mathematical Reviews (MathSciNet): MR49:1423
Zentralblatt MATH: 0322.58001
[GKRS] Benedict Gross, Bertram Kostant, Pierre Ramond, and Shlomo Sternberg, The Weyl character formula, the half-spin representations,and equal rank subgroups, Proc. Natl. Acad. Sci. USA 95 (1998), no. 15, 8441–8442 (electronic).
Mathematical Reviews (MathSciNet): MR99f:17007
Zentralblatt MATH: 0918.17002
Digital Object Identifier: doi:10.1073/pnas.95.15.8441
[He] Sigurdur Helgason, Groups and geometric analysis, Pure and Applied Mathematics, vol. 113, Academic Press Inc., Orlando, FL, 1984.
Mathematical Reviews (MathSciNet): MR86c:22017
Zentralblatt MATH: 0543.58001
[Hi] F. Hirzebruch, Topological methods in algebraic geometry, Third enlarged edition. New appendix and translation from the second German edition by R. L. E. Schwarzenberger, with an additional section by A. Borel. Die Grundlehren der Mathematischen Wissenschaften, Band 131, Springer-Verlag New York, Inc., New York, 1966.
Mathematical Reviews (MathSciNet): MR34:2573
Zentralblatt MATH: 0138.42001
[Ka] Max Karoubi, $K$-theory, Springer-Verlag, Berlin, 1978.
Mathematical Reviews (MathSciNet): MR58:7605
Zentralblatt MATH: 0382.55002
[KS] Yoichi Kazama and Hisao Suzuki, New $N=2$ superconformal field theories and superstring compactification, Nuclear Phys. B 321 (1989), no. 1, 232–268.
Mathematical Reviews (MathSciNet): MR90g:81249
Digital Object Identifier: doi:10.1016/0550-3213(89)90250-2
[Ko1] Bertram Kostant, Lie algebra cohomology and the generalized Borel-Weil theorem, Ann. of Math. (2) 74 (1961), 329–387.
Mathematical Reviews (MathSciNet): MR26:265
Zentralblatt MATH: 0134.03501
Digital Object Identifier: doi:10.2307/1970237
JSTOR: links.jstor.org
[Ko2] Bertram Kostant, Clifford algebra analogue of the Hopf-Koszul-S amelson theorem, the $\rho$-decomposition $C(\germ g)=\rm End\,V\sb \rho \otimes C(P)$, and the $\germ g$-module structure of $\bigwedge \germ g$, Adv. Math. 125 (1997), no. 2, 275–350.
Mathematical Reviews (MathSciNet): MR98k:17009
Zentralblatt MATH: 0882.17002
Digital Object Identifier: doi:10.1006/aima.1997.1608
[LVW] Wolfgang Lerche, Cumrun Vafa, and Nicholas P. Warner, Chiral rings in $N=2$ superconformal theories, Nuclear Phys. B 324 (1989), no. 2, 427–474.
Mathematical Reviews (MathSciNet): MR91d:81132
Digital Object Identifier: doi:10.1016/0550-3213(89)90474-4
[P] R. Parthasarathy, Dirac operator and the discrete series, Ann. of Math. (2) 96 (1972), 1–30.
Mathematical Reviews (MathSciNet): MR47:6945
Zentralblatt MATH: 0249.22003
Digital Object Identifier: doi:10.2307/1970892
[S1] Stephen Slebarski, The Dirac operator on homogeneous spaces and representations of reductive Lie groups. I, Amer. J. Math. 109 (1987), no. 2, 283–301.
Mathematical Reviews (MathSciNet): MR89a:22028
Zentralblatt MATH: 0649.58031
Digital Object Identifier: doi:10.2307/2374575
JSTOR: links.jstor.org
[S2] Stephen Slebarski, The Dirac operator on homogeneous spaces and representations of reductive Lie groups. II, Amer. J. Math. 109 (1987), no. 3, 499–520.
Mathematical Reviews (MathSciNet): MR88g:22015
Zentralblatt MATH: 0669.22003
Digital Object Identifier: doi:10.2307/2374565
JSTOR: links.jstor.org
[W] N. Wallach, personal conversation, 1999, February.
Duke Mathematical Journal