TY - JOUR
T1 - Irreducible characters of general linear superalgebra and super duality
AU - Cheng, Shun Jen
AU - Lam, Ngau
N1 - Funding Information:
Partially supported by an NSC-grant and an Academia Sinica Investigator grant.
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
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U2 - 10.1007/s00220-010-1087-7
DO - 10.1007/s00220-010-1087-7
M3 - Article
AN - SCOPUS:77954956265
SN - 0010-3616
VL - 298
SP - 645
EP - 672
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 3
ER -