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＜E-Book＞
Singular Loci of Schubert Varieties / by Sara Sarason, V. Lakshmibai
(Progress in Mathematics. ISSN:2296505X ; 182)

Edition	1st ed. 2000.
Publisher	Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser
Year	2000
Language	English
Size	XII, 251 p : online resource
Authors	*Sarason, Sara author Lakshmibai, V author SpringerLink (Online service)
Subjects	LCSH:Algebraic geometry LCSH:Topological groups LCSH:Lie groups LCSH:Discrete mathematics LCSH:Geometry, Differential FREE:Algebraic Geometry FREE:Topological Groups and Lie Groups FREE:Discrete Mathematics FREE:Differential Geometry
Notes	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 "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 HTTP:URL=https://doi.org/10.1007/978-1-4612-1324-6

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