Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

A NOTE ON THE VARIETY OF PROJECTORS

Tools
- Tools
+ Tools

UNSPECIFIED (1991) A NOTE ON THE VARIETY OF PROJECTORS. JOURNAL OF PURE AND APPLIED ALGEBRA, 74 (1). pp. 73-84.

Research output not available from this repository, contact author.

Request Changes to record.

Abstract

Somewhat analogous to the case of the variety of Complexes, the variety P of projectors, i.e., idempotents (of rank d on an n-space), 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 H-invariants 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): m-omega-d X m-omega-n-d X (-m) det., m element-of Z+, where omega-d and omega-n-d 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: 0022-4049
Official Date: 10 September 1991
Dates:
DateEvent
10 September 1991UNSPECIFIED
Volume: 74
Number: 1
Number of Pages: 12
Page Range: pp. 73-84
Publication Status: Published

Data sourced from Thomson Reuters' Web of Knowledge

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item
twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us