Irreducible Characters of General Linear Superalgebra and Super Duality

By Shun-Jen Cheng, Ngau Lam. 2009

55 citations recorded by the source corpus.

We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating the problem to the classical Kazhdan-Lusztig theory. Furthermore, we prove that certain parabolic BGG categories over the general linear algebra and over the general linear superalgebra are equivalent. We also verify a parabolic version of a conjecture of Brundan on the irreducible characters in the BGG category of the general linear superalgebra.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b442d4ed7cc67235b91fa619d3982d7184ceb601

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Citations in the corpus

Cohomology of generalized supergrassmannians and character formulae for basic classical Lie superalgebras (2009, methodology): “lved this problem by a diﬀerent, purely algebraic, method and discovered a remarkable connection with the representation theory of gl(∞). Brundan’s method was developed further in [8], [4], [5], [6], [7]. Inthispaperwegeneralise the methodof [24]to the orthosymplectic groupsOSP(m,2n). The results we”
Highest weight categories arising from Khovanov's diagram algebra II: Koszulity (2008, background): “ representation theory of (walled) Brauer algebras. On the supergroup side (Paper IV), a more direct proof of the super duality conjecture of Cheng, Wang and Zhang has now been found by Cheng and Lam [CL]. Also our diagrammatics for GL(m|n) has been extended to cover blocks of the orthosymplectic su”
Highest weight categories arising from Khovanov's diagram algebra IV: the general linear supergroup (2009, background): “A direct algebraic proof of this conjecture, and its substantial generalisation from [CW], has recently been found by Cheng and Lam [ CL ].”