Certain topics on the representation theory of the Lie algebra \(gl(\lambda)\)

DOI10.1007/BF02434006zbMath0916.17019WikidataQ115392190 ScholiaQ115392190MaRDI QIDQ1281947

Boris Shoikhet

Publication date: 25 March 1999

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

zbMATH Keywords

irreducible representationcombinatorial identitiesinfinite-dimensional Lie algebraJantzen filtrationinduced representationShapovalov form

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Lie algebras of vector fields and related (super) algebras (17B66) Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras (17-02)

Related Items

Algebra gl(λ) Inside the Algebra of Differential Operators on the Real Line, The Shapovalov Determinant for the Poisson Superalgebras, Shapovalov determinant for loop superalgebras, Graded Lie algebras whose Cartan subalgebra is the algebra of polynomials in one variable

Cites Work

• Structure of representations with highest weight of infinite-dimensional Lie algebras
• Kontravariante Formen auf induzierten Darstellungen halbeinfacher Lie-Algebren
• Quasifinite highest weight modules over the Lie algebra of differential operators on the circle
• Structure of representations generated by vectors of highest weight
• Canonical factorization of continuous operator functions relative to the circle
• UNITARY REPRESENTATIONS OF NILPOTENT LIE GROUPS
• Filtrations on Verma modules
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