Singular loci of Schubert varieties
Author(s)
Bibliographic Information
Singular loci of Schubert varieties
（Progress in mathematics, v. 182）
Birkhäuser, c2000
- : us
- : sz
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
Includes bibliographical references (p. [239]-245) and index
Description and Table of Contents
- Volume
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: us ISBN 9780817640927
Description
"Singular Loci of Schubert Varieties" is a unique work at the crossroads of representation theory, algebraic geometry, and combinatorics. Over the past 20 years, many research articles have been written on the subject in notable journals. In this work, Billey and Lakshmibai have recreated and restructured the various theories and approaches of those articles and present a clearer understanding of this important subdiscipline of Schubert varieties - namely singular loci. The main focus, therefore, is on the computations for the singular loci of Schubert varieties and corresponding tangent spaces. The methods used include standard monomial theory, the nil Hecke ring, and Kazhdan-Lusztig theory. New results are presented with sufficient examples to emphasize key points. A comprehensive bibliography, index, and tables - the latter not to be found elsewhere in the mathematics literature - round out this concise work. After a good introduction giving background material, the topics are presented in a systematic fashion to engage a wide readership of researchers and graduate students.
Table of Contents
1. Introduction.- 2. Generalities on G/B and G/Q.- 3. Specifics for the Classical Groups.- 4. The Tangent Space and Smoothness.- 5. Root System Description of T(w, ?).- 6. Rational Smoothness and Kazhdan-Lusztig Theory.- 7. Nil-Hecke Ring and the Singular Locus of X(w).- 8. Patterns, Smoothness and Rational Smoothness.- 9. Minuscule and cominuscule G/P.- 10. Rank Two Results.- 11. Related Combinatorial Results.- 12. Related Varieties.- 13. Addendum.
- Volume
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: sz ISBN 9783764340926
Description
This text presents topics in a systematic fashion to engage a wide readership. It includes: generalities on G/B and G/Q; the Grassmannian and the flag variety SL_n/B' the tangent space and smoothness; rational smoothness and Kazhdan-Lusztig theory; and root system description of T (w,/tau).
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