Lakshmibai, V. ; Raghavan, K. N. ; Sankaran, P. ; Shukla, P.
(2006)
*Standard monomial bases, moduli spaces of vector bundles, and invariant theory*
Transformation Groups, 11
(4).
pp. 673-704.
ISSN 1083-4362

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Official URL: http://www.springerlink.com/content/y1636737m5v308...

Related URL: http://dx.doi.org/10.1007/s00031-005-1123-4

## Abstract

Consider the diagonal action of SO_{n}(K) on the affine space X=V^{⊕m} where V=K^{n}, K an algebraically closed field of characteristic ≠ 2. We construct a "standard monomial" basis for the ring of invariants K[X]^{SOn(K)*}. As a consequence, we deduce that K[X]^{SOn(K)} is Cohen-Macaulay. As the first application, we present the first and second fundamental theorems for SO_{n}(K)-actions. As the second application, assuming that the characteristic of K is ≠ 2,3, we give a characteristic-free proof of the Cohen-Macaulayness of the moduli space M_{2} of equivalence classes of semi-stable, rank 2, −1760 vector bundles on a smooth projective curve of genus 7gt; 2. As the third application, we describe a K-basis for the ring of invariants for the adjoint action of SL_{2}(K) on m copies of sl_{2}(K) in terms of traces.

Item Type: | Article |
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Source: | Copyright of this article belongs to Springer. |

ID Code: | 57699 |

Deposited On: | 29 Aug 2011 08:23 |

Last Modified: | 06 Jul 2012 05:28 |

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