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001 978-981-10-6391-6
003 DE-He213
005 20181204134423.0
007 cr nn 008mamaa
008 171016s2017 si | s |||| 0|eng d
020 _a9789811063916
_9978-981-10-6391-6
024 7 _a10.1007/978-981-10-6391-6
_2doi
040 _aISI Library, Kolkata
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512
_223
100 1 _aXu, Xiaoping.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aRepresentations of Lie Algebras and Partial Differential Equations
_h[electronic resource] /
_cby Xiaoping Xu.
264 1 _aSingapore :
_bSpringer Singapore :
_bImprint: Springer,
_c2017.
300 _aXXXVI, 620 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPreface.- Introduction.- I   Fundament of Lie Algebras.- Preliminary of Lie Algebras.- Semisimple Lie Algebras.-  Root Systems.-  Isomorphisms, Conjugacy and Exceptional Types.- Highest-Weight Representation Theory.- II    Explicit Representations.- Representations of Special Linear Algebras.-  Representations of Even Orthogonal Lie Algebras --  Representations of Odd Orthogonal Lie Algebras -- Representations of Symplectic Lie Algebras --  Representations of G 2 and F 4 -- Representations of E6 -- Representations of E -- III    Related Topics -- Oscillator Representations of gl(n | m) and osp(n | 2m) -- Representation Theoretic Codes -- Path Hypergeometric Functions -- Bibliography -- Index. .
520 _aThis book provides explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic codes, combinatorics and algebraic varieties, summarizing the author’s works and his joint works with his former students.  Further, it presents various oscillator generalizations of the classical representation theorem on harmonic polynomials, and highlights new functors from the representation category of a simple Lie algebra to that of another simple Lie algebra. Partial differential equations play a key role in solving certain representation problems. The weight matrices of the minimal and adjoint representations over the simple Lie algebras of types E and F are proved to generate ternary orthogonal linear codes with large minimal distances. New multi-variable hypergeometric functions related to the root systems of simple Lie algebras are introduced in connection with quantum many-body systems in one dimension. In addition, the book identifies certain equivalent combinatorial properties on representation formulas, and the irreducibility of representations is proved directly related to algebraic varieties. The book offers a valuable reference guide for mathematicians and scientists alike. As it is largely self-contained – readers need only a minimal background in calculus and linear algebra – it can also be used as a textbook.
650 0 _aAlgebra.
650 0 _aDifferential equations, partial.
650 0 _aFunctions, special.
650 0 _aAlgorithms.
650 1 4 _aAlgebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11000
650 2 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
650 2 4 _aSpecial Functions.
_0http://scigraph.springernature.com/things/product-market-codes/M1221X
650 2 4 _aAlgorithms.
_0http://scigraph.springernature.com/things/product-market-codes/M14018
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9789811063909
776 0 8 _iPrinted edition:
_z9789811063923
856 4 0 _uhttps://doi.org/10.1007/978-981-10-6391-6
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c427365
_d427365