Translator Disclaimer
1 June 2006 A bound for canonical dimension of the (semi)spinor groups
Nikita A. Karpenko
Author Affiliations +
Duke Math. J. 133(2): 391-404 (1 June 2006). DOI: 10.1215/S0012-7094-06-13328-8

Abstract

Using the theory of nonnegative intersections, duality of the Schubert varieties, and a Pieri-type formula for the varieties of maximal, totally isotropic subspaces, we get an upper bound for the canonical dimension cd(Spinn) of the spinor group Spinn. A lower bound is given by the canonical 2-dimension cd2(Spinn), computed in [10]. If n or n+1 is a power of 2, no space is left between these two bounds; therefore, the precise value of cd(Spinn) is obtained for such n. We also produce an upper bound for canonical dimension of the semispinor group (giving the precise value of the canonical dimension in the case when the rank of the group is a power of 2) and show that spinor and semispinor groups are the only open cases of the question about canonical dimension of an arbitrary simple split group possessing a unique torsion prime

Citation

Download Citation

Nikita A. Karpenko. "A bound for canonical dimension of the (semi)spinor groups." Duke Math. J. 133 (2) 391 - 404, 1 June 2006. https://doi.org/10.1215/S0012-7094-06-13328-8

Information

Published: 1 June 2006
First available in Project Euclid: 21 May 2006

zbMATH: 1100.14038
MathSciNet: MR2225698
Digital Object Identifier: 10.1215/S0012-7094-06-13328-8

Subjects:
Primary: 14C25, 14L17

Rights: Copyright © 2006 Duke University Press

JOURNAL ARTICLE
14 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.133 • No. 2 • 1 June 2006
Back to Top