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Author : Gregory Saunders Warrington
Release : 2001
Genre : Kazhdan-Lusztig polynomials
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Kazhdan-Lusztig Polynomials, Pattern Avoidance and Singular Loci of Schubert Varieties by : Gregory Saunders Warrington
Download or read book Kazhdan-Lusztig Polynomials, Pattern Avoidance and Singular Loci of Schubert Varieties written by Gregory Saunders Warrington. This book was released on 2001. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Sara Sarason
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 24X/5 ( reviews)
Book Synopsis Singular Loci of Schubert Varieties by : Sara Sarason
Download or read book Singular Loci of Schubert Varieties written by Sara Sarason. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Author : Anders Bjorner
Release : 2006-02-25
Genre : Mathematics
Kind : eBook
Book Rating : 967/5 ( reviews)
Book Synopsis Combinatorics of Coxeter Groups by : Anders Bjorner
Download or read book Combinatorics of Coxeter Groups written by Anders Bjorner. This book was released on 2006-02-25. Available in PDF, EPUB and Kindle. Book excerpt: Includes a rich variety of exercises to accompany the exposition of Coxeter groups Coxeter groups have already been exposited from algebraic and geometric perspectives, but this book will be presenting the combinatorial aspects of Coxeter groups
Author : Laurent Manivel
Release : 2001
Genre : Computers
Kind : eBook
Book Rating : 541/5 ( reviews)
Book Synopsis Symmetric Functions, Schubert Polynomials and Degeneracy Loci by : Laurent Manivel
Download or read book Symmetric Functions, Schubert Polynomials and Degeneracy Loci written by Laurent Manivel. This book was released on 2001. Available in PDF, EPUB and Kindle. Book excerpt: This text grew out of an advanced course taught by the author at the Fourier Institute (Grenoble, France). It serves as an introduction to the combinatorics of symmetric functions, more precisely to Schur and Schubert polynomials. Also studied is the geometry of Grassmannians, flag varieties, and especially, their Schubert varieties. This book examines profound connections that unite these two subjects. The book is divided into three chapters. The first is devoted to symmetricfunctions and especially to Schur polynomials. These are polynomials with positive integer coefficients in which each of the monomials correspond to a Young tableau with the property of being ``semistandard''. The second chapter is devoted to Schubert polynomials, which were discovered by A. Lascoux andM.-P. Schutzenberger who deeply probed their combinatorial properties. It is shown, for example, that these polynomials support the subtle connections between problems of enumeration of reduced decompositions of permutations and the Littlewood-Richardson rule, a particularly efficacious version of which may be derived from these connections. The final chapter is geometric. It is devoted to Schubert varieties, subvarieties of Grassmannians, and flag varieties defined by certain incidenceconditions with fixed subspaces. This volume makes accessible a number of results, creating a solid stepping stone for scaling more ambitious heights in the area. The author's intent was to remain elementary: The first two chapters require no prior knowledge, the third chapter uses some rudimentary notionsof topology and algebraic geometry. For this reason, a comprehensive appendix on the topology of algebraic varieties is provided. This book is the English translation of a text previously published in French.
Author : William M. McGovern
Release : 2022-11-07
Genre : Mathematics
Kind : eBook
Book Rating : 949/5 ( reviews)
Book Synopsis Representation Theory and Geometry of the Flag Variety by : William M. McGovern
Download or read book Representation Theory and Geometry of the Flag Variety written by William M. McGovern. This book was released on 2022-11-07. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive reference begins with a review of the basics followed by a presentation of flag varieties and finite- and infinite-dimensional representations in classical types and subvarieties of flag varieties and their singularities. Associated varieties and characteristic cycles are covered as well and Kazhdan-Lusztig polynomials are treated. The coverage concludes with a discussion of pattern avoidance and singularities and some recent results on Springer fibers.
