000			02489nam 2200349| 4500
001			85766
005			20210922162525.0
010			_a978-981-13-1393-6 _dcompra
090			_a85766
100			_a20190128d2018 k||y0pory50 ba
101	0		_aeng
102			_aUS
200	1		_aFlag varieties _bDocumento electrónico _dan interplay of geometry, combinatorics, and representation theory _fV. Lakshmibai, Justin Brown
210			_aSingapore _cSpringer Singapore _cSpringer _d2018
215			_aXIV, 312 p.
225	2		_aTexts and Readings in Mathematics
300			_aColocação: Online
303			_aThis book discusses the importance of flag varieties in geometric objects and elucidates its richness as interplay of geometry, combinatorics and representation theory. The book presents a discussion on the representation theory of complex semisimple Lie algebras, as well as the representation theory of semisimple algebraic groups. In addition, the book also discusses the representation theory of symmetric groups. In the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Many of the geometric results admit elegant combinatorial description because of the root system connections, a typical example being the description of the singular locus of a Schubert variety. This discussion is carried out as a consequence of standard monomial theory. Consequently, this book includes standard monomial theory and some important applications—singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. The two recent results on Schubert varieties in the Grassmannian have also been included in this book. The first result gives a free resolution of certain Schubert singularities. The second result is about certain Levi subgroup actions on Schubert varieties in the Grassmannian and derives some interesting geometric and representation-theoretic consequences.
410	1		_x2366-8717 _v53
606			_aGeometria algébrica
606			_aAnéis (Álgebra)
606			_aAnéis associativos
606			_aTeoria dos grupos
680			_aQA564
700			_aLakshmibai _bV.
702			_933770 _aBrown _bJustin _4070
801		0	_gRPC _aPT
856			_uhttps://doi.org/10.1007/978-981-13-1393-6
942			_2lcc _cF _n0