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ISBN: 1493930818 1493930826 9781493930821 Year: 2015 Publisher: New York, NY : Springer New York : Imprint: Springer,
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This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads of commutative algebra, algebraic geometry, representation theory, and combinatorics. Therefore, this text uniquely presents an exciting playing field for graduate students and researchers in mathematics, physics, and computer science, to expand their knowledge in the field of algebraic geometry. The standard monomial theory (SMT) for the Grassmannian varieties and their Schubert subvarieties are introduced and the text presents some important applications of SMT including the Cohen–Macaulay property, normality, unique factoriality, Gorenstein property, singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. This text would serve well as a reference book for a graduate work on Grassmannian varieties and would be an excellent supplementary text for several courses including those in geometry of spherical varieties, Schubert varieties, advanced topics in geometric and differential topology, representation theory of compact and reductive groups, Lie theory, toric varieties, geometric representation theory, and singularity theory. The reader should have some familiarity with commutative algebra and algebraic geometry.
Geometry --- Mathematics --- Physical Sciences & Mathematics --- Representations of groups. --- Geometry. --- Group representation (Mathematics) --- Groups, Representation theory of --- Mathematics. --- Algebraic geometry. --- Algebraic topology. --- Combinatorics. --- Algebraic Geometry. --- Algebraic Topology. --- Euclid's Elements --- Group theory --- Geometry, algebraic. --- Combinatorics --- Algebra --- Mathematical analysis --- Topology --- Algebraic geometry --- Combinatorics & graph theory. --- Math --- Science
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ISBN: 3319234420 3319234439 Year: 2015 Publisher: Cham : Springer International Publishing : Imprint: Birkhäuser,
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Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups. His groundbreaking ideas have lead to deep advances in the theory of real and p-adic groups, and have forged lasting connections with other subjects, including number theory, automorphic forms, algebraic geometry, and combinatorics. Representations of Reductive Groups is an outgrowth of the conference of the same name, dedicated to David Vogan on his 60th birthday, which took place at MIT on May 19-23, 2014. This volume highlights the depth and breadth of Vogan's influence over the subjects mentioned above, and point to many exciting new directions that remain to be explored. Notably, the first article by McGovern and Trapa offers an overview of Vogan's body of work, placing his ideas in a historical context. Contributors: Pramod N. Achar, Jeffrey D. Adams, Dan Barbasch, Manjul Bhargava, Cédric Bonnafé, Dan Ciubotaru, Meinolf Geck, William Graham, Benedict H. Gross, Xuhua He, Jing-Song Huang, Toshiyuki Kobayashi, Bertram Kostant, Wenjing Li, George Lusztig, Eric Marberg, William M. McGovern, Wilfried Schmid, Kari Vilonen, Diana Shelstad, Peter E. Trapa, David A. Vogan, Jr., Nolan R. Wallach, Xiaoheng Wang, Geordie Williamson.
Algebra --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Representations of groups --- Linear algebraic groups. --- Data processing. --- Algebraic groups, Linear --- Group representation (Mathematics) --- Groups, Representation theory of --- Mathematics. --- Algebraic geometry. --- Topological groups. --- Lie groups. --- Number theory. --- Topological Groups, Lie Groups. --- Algebraic Geometry. --- Number Theory. --- Group theory --- Geometry, Algebraic --- Algebraic varieties --- Topological Groups. --- Geometry, algebraic. --- Number study --- Numbers, Theory of --- Algebraic geometry --- Geometry --- Groups, Topological --- Continuous groups --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups
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