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A NOTE ON THE VARIETY OF PROJECTORS
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UNSPECIFIED. (1991) A NOTE ON THE VARIETY OF PROJECTORS. JOURNAL OF PURE AND APPLIED ALGEBRA, 74 (1). pp. 7384. ISSN 00224049
Full text not available from this repository.Abstract
Somewhat analogous to the case of the variety of Complexes, the variety P of projectors, i.e., idempotents (of rank d on an nspace), is shown to be a principal affine open subset of the product of the Grassmannian Gr(d, n) and its dual Gr(n  d, n). Also P is identified with the affine coset space GL(n)/H for a closed reductive subgroup H of the form GL(d) x GL(n  d); consequently, P is nonsingular and of dimension 2d(n  d). The coordinate ring R of P is described explicitly by generators and relations as the subring of left translation Hinvariants of k[GL(n)] as an immediate consequence of the classical Hodge Standard Monomial Basis readily available for R just as for the homogeneous coordinate ring of Gr(d, n) for its Plucker embedding. The GL(n)module structure of R is shown to be the direct limit of the filtered family of representations of GL(n): momegad X momegand X (m) det., m elementof Z+, where omegad and omegand are the fundamental weights of GL(n) corresponding to Gr(d, n) and Gr(n  d, n), respectively, and det. is the determinant character of GL(n).
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics  
Journal or Publication Title:  JOURNAL OF PURE AND APPLIED ALGEBRA  
Publisher:  ELSEVIER SCIENCE BV  
ISSN:  00224049  
Official Date:  10 September 1991  
Dates: 


Volume:  74  
Number:  1  
Number of Pages:  12  
Page Range:  pp. 7384  
Publication Status:  Published  
URI:  http://wrap.warwick.ac.uk/id/eprint/22447 
Data sourced from Thomson Reuters' Web of Knowledge
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