02545cam a2200433Ii 4500 3084 3084 OSt 20210813061105.0 180702s2018 si a ob 001 0 eng d 9789811313936 9811313938 ALUPE UNIVERSITY CLYY QA564 .L24 2018 Lakshmibai, V. Flag varieties : an interplay of geometry, combinatorics, and representation theory / V. Lakshmibai, Justin Brown Second edition Singapore : Springer, 2018 1 online resource (xiv, 312 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Includes bibliographical references and index 880-01 Provided by publisher Online resource; title from PDF title page (SpringerLink, viewed July 2, 2018) UCLA Library - CDL shared resource. Flag manifolds Geometry, Algebraic Representations of groups Schubert varieties Semisimple Lie groups Brown, Justin (Justin Allen), author 53. 2366-8717 505-00/(S 3.3 Ordinary Representations3.4 Tensor Product of Representations; 3.5 Contragradient Representations; 3.6 Restrictions and Inductions; 3.7 Character Group of G; Exercises; 4 Representation Theory of the Symmetric Group; 4.1 The Symmetric Group Sn; 4.2 Frobenius-Young Modules; 4.3 Specht Modules; 4.4 General Case; 4.5 Proof of Theorem 4.3.7; 4.6 Representation Theory of An; Exercises; 5 Symmetric Polynomials; 5.1 Notation and Motivation; 5.2 Several Bases for S (n); 5.3 Kostka Numbers & Determinantal Formulas; 5.4 Results x(Sn(B; Exercises 505-01/(S 10.1 Cartan Subgroups10.2 The Weyl Group; 10.3 Regular and Singular Tori; 10.4 Semisimple Rank 1; 10.5 One Parameter Subgroups; 10.6 Reductive Groups; 10.7 Almost Simple Groups; 10.8 Schubert Varieties & Bruhat Decomposition; 10.9 Standard Parabolic Subgroups; Exercises; 11 Representation Theory of Semisimple Algebraic Groups; 11.1 Weight Vectors; 11.2 Geometric Realization of V((Sn(B); 12 Geometry of the Grassmannian, Flag and their Schubert Varieties via Standard Monomial Theory; 12.1 Grassmannian Variety; 12.2 Gd, n Identified with a Homogeneous Space; 12.3 Schubert Varieties cdl 190227 lcc BK PW 0 0 lcc 0 0 MLIB MLIB OS 2021-08-13 DONATION FROM MOI UNIVERSITY 0 QA564 .L24 2018 28004155 2021-08-13 2021-08-13 BK PW