Standard monomial bases, moduli spaces of vector bundles, and invariant theory

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 SOn(K) on the affine space X=V⊕m where V=Kn, 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 SOn(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 M2 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 SL2(K) on m copies of sl2(K) in terms of traces.

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Deposited On:29 Aug 2011 08:23
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