Kazhdan-Lusztig Polynomials and Character Formula for the Lie Superalgebra $\frak {gl}(m|n)$

1996 ◽  
Vol 2 (4) ◽  
pp. 607-651 ◽  
Author(s):  
V. Serganova
Keyword(s):  
Lie Superalgebra ◽  
Character Formula ◽  
Lusztig Polynomials

CHARACTERS OF STRONGLY GENERIC IRREDUCIBLE LIE SUPERALGEBRA REPRESENTATIONS

1998 ◽  
Vol 09 (03) ◽  
pp. 331-366 ◽  
Author(s):  
IVAN PENKOV
Keyword(s):  
Lie Superalgebra ◽  
Character Formula ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Simple Component

An explicit character formula is established for any strongly generic finite-dimensional irreducible [Formula: see text]-module, [Formula: see text] being an arbitrary finite-dimensional complex Lie superalgebra. This character formula had been conjectured earlier by Vera Serganova and the author for any generic irreducible finite-dimensional [Formula: see text]-module, i.e. such that its highest weight is far enough from the walls of the Weyl chambers. The condition of strong genericity, under which the conjecture is proved in this paper, is slightly stronger than genericity, but if in particular no simple component of [Formula: see text] is isomorphic to psq(n) for n ≥ 3 or to H(2k + 1) for k ≥ 2, strong genericity is equivalent to genericity.

A character formula for singly atypical modules of the lie superalgebra sl(m/n)

1990 ◽  
Vol 18 (10) ◽  
pp. 3453-3480 ◽  
Author(s):  
J. Van der Jeugt ◽  
J.W.B. Hughes ◽  
R.C. King ◽  
J. Thierry-Mieg
Keyword(s):  
Lie Superalgebra ◽  
Character Formula

Characters and quantum reduction for orthosymplectic Lie superalgebras

2021 ◽  
Author(s):  
Namhee Kwon
Keyword(s):  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Character Formula ◽  
Quantum Reduction

In this study, we study principal admissible representations for the affine Lie superalgebra [Formula: see text]. Using the character formula of irreducible admissible representations of [Formula: see text], we calculate a character formula of [Formula: see text]-modules which are obtained from the quantized Drinfeld–Sokolov reduction and principal admissible representations. As a by-product, we obtain the minimal series modules of the Neveu–Schwarz algebra through the [Formula: see text]-modules arising from the principal admissible modules over [Formula: see text].

Cartan invariants for the Witt superalgebra W(2) in positive characteristic

2016 ◽  
Vol 15 (03) ◽  
pp. 1650039 ◽  
Author(s):  
Feifei Duan ◽  
Fang Li
Keyword(s):  
Positive Characteristic ◽  
Lie Superalgebra ◽  
Character Formula ◽  
Closed Field ◽  
Projective Modules ◽  
Algebraically Closed Field ◽  
Grassmann Superalgebra ◽  
Cartan Invariants

The aim of this paper is to study the projective modules of the [Formula: see text]-reduced enveloping superalgebra [Formula: see text], where [Formula: see text] is the Lie superalgebra of superderivations on the Grassmann superalgebra [Formula: see text], over an algebraically closed field k of characteristic [Formula: see text]. Mainly, the Cartan invariants and the dimensions of indecomposable projective modules of [Formula: see text] are determined for any [Formula: see text]-character [Formula: see text] up to isomorphism.

Sign in / Sign up

Export Citation Format

Share Document