000			02116nam a2200349Ia 4500
003			OSt
005			20250125154348.0
008			241112s9999 xx 000 0 und d
020			_a9789386279705 (hbk.) _c₹ 900.00
040			_bENG _cIISER-BPR
041			_aENG
082			_a516.35 _bLAK _223rd
100			_aLakshmibai, V. _91093
222			_aMathematics
245		0	_aFlag varieties : _bAn interplay of geometry, combinatorics and representation theory.
250			_a2nd ed.
260			_aNew Delhi: _bHindustan Book Agency, _cc2018.
300			_axiii, 310p. : _c24cm
440			_aTexts and Readings in Mathematics _vVol. 53 _92633
504			_aIncludes appendix, bibliographic references, list of symbols and subject index.
520			_aFlag varieties are important geometric objects and their study involves an interplay of geometry, combinatorics, and representation theory. This book is detailed account of this interplay. In the area of representation theory, the book presents a discussion of complex semisimple Lie algebras and of semisimple algebraic groups; in addition, the representation theory of symmetric groups is also discussed. In the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Because of the connections with root systems, many of the geometric results admit elegant combinatorial description, a typical example being the description of the singular locus of a Schubert variety. This is shown to be a consequence of standard monomial theory (abbreviated SMT). Thus the book includes SMT and some important applications - singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory.
650			_aMathematics _92634
650			_aGeometry _92635
650			_aAlgebraic geometry _92636
650			_aCombinatorics _92637
650			_aRepresentation theory _92638
700			_aBrown, Justin _92639
942			_cBK _2ddc
942			_2ddc
947			_a900
948			_a22
999			_c4233 _d4233