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Titlebook: Singular Loci of Schubert Varieties; Sara Billey,V. Lakshmibai Book 2000 Springer Science+Business Media New York 2000 Algebra and differe

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发表于 2025-3-21 18:48:12 | 显示全部楼层 |阅读模式
书目名称Singular Loci of Schubert Varieties
编辑Sara Billey,V. Lakshmibai
视频video
丛书名称Progress in Mathematics
图书封面Titlebook: Singular Loci of Schubert Varieties;  Sara Billey,V. Lakshmibai Book 2000 Springer Science+Business Media New York 2000 Algebra and differe
描述."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..
出版日期Book 2000
关键词Algebra and differential geometry; Graph; Node; Representation theory; combinatorics; lie groups; topologi
版次1
doihttps://doi.org/10.1007/978-1-4612-1324-6
isbn_softcover978-1-4612-7094-2
isbn_ebook978-1-4612-1324-6Series ISSN 0743-1643 Series E-ISSN 2296-505X
issn_series 0743-1643
copyrightSpringer Science+Business Media New York 2000
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发表于 2025-3-21 20:14:34 | 显示全部楼层
Introduction,then Chevalley, and later Bernstein, Gelfand, Gelfand and Demazure. Schubert varieties are now some of the best understood examples of complex projective varieties in the literature. Therefore, they play an important role in current mathematical research. Outside of mathematics, their applications a
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Generalities on , and ,, theory for semisimple algebraic groups. For more details on root systems and Weyl groups, we recommend Humphrey’s . [.] and . [.]. Other references for this chapter are Bourbaki’s ., . 4, . [.], Borel’s . [.], Humphrey’s . [.], and Jantzen’s . [.].
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Specifics for the Classical Groups, out the generalities considered in the previous chapter for the semisimple group . (.).We first review the results for the Grassmannians; we then review the results for .(.). For more details, one may refer to [., .]. Important details for the other classical groups .(2.),.(2. + 1), and .(2.)are al
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Nil-Hecke Ring and the Singular Locus of ,(,),state and prove Kumar’s criteria for smoothness and rational smoothness at T-fixed points. The proof hinges on the relation between the nil-Hecke ring and the formal . character of the ring of functions on the scheme theoretic tangent cone ..... We also include Dyer’s proof of Deodhar’s inequality h
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