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020 _a9789811018138
_9978-981-10-1813-8
024 7 _a10.1007/978-981-10-1813-8
_2doi
040 _aISI Library, Kolkata
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
082 0 4 _a516.35
_223
100 1 _aSeshadri, C. S.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aIntroduction to the Theory of Standard Monomials
_h[electronic resource] :
_bSecond Edition /
_cby C. S. Seshadri.
264 1 _aSingapore :
_bSpringer Singapore :
_bImprint: Springer,
_c2016.
300 _aXVI, 224 p. 20 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aTexts and Readings in Mathematics,
_x2366-8717 ;
_v46
505 0 _aChapter 1. Schubert Varieties in the Grassmannian -- Chapter 2. Standard monomial theory on SLn(k)/Q -- Chapter 3. Applications -- Chapter 4. Schubert varieties in G/Q.
520 _aThe book is a reproduction of a course of lectures delivered by the author in 1983-84 which appeared in the Brandeis Lecture Notes series. The aim of this course was to give an introduction to the series of papers by concentrating on the case of the full linear group. In recent years, there has been great progress in standard monomial theory due to the work of Peter Littelmann. The author’s lectures (reproduced in this book) remain an excellent introduction to standard monomial theory. d-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;">Standard monomial theory deals with the construction of nice bases of finite dimensional irreducible representations of semi-simple algebraic groups or, in geometric terms, nice bases of coordinate rings of flag varieties (and their Schubert subvarieties) associated with these groups. Besides its intrinsic interest, standard monomial theory has applications to the study of the geometry of Schubert varieties. Standard monomial theory has its origin in the work of Hodge, giving bases of the coordinate rings of the Grassmannian and its Schubert subvarieties by “standard monomials”. In its modern form, standard monomial theory was developed by the author in a series of papers written in collaboration with V. Lakshmibai and C. Musili. In the second edition of the book, conjectures of a standard monomial theory for a general semi-simple (simply-connected) algebraic group, due to Lakshmibai, have been added as an appendix, and the bibliography has been revised.
650 0 _aGeometry, algebraic.
650 0 _aField theory (Physics).
650 1 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
650 2 4 _aField Theory and Polynomials.
_0http://scigraph.springernature.com/things/product-market-codes/M11051
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9789811018121
776 0 8 _iPrinted edition:
_z9789811018145
830 0 _aTexts and Readings in Mathematics,
_x2366-8717 ;
_v46
856 4 0 _uhttps://doi.org/10.1007/978-981-10-1813-8
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c426592
_d426592