scholarly journals Staggered and affine Kac modules over A1(1)

2020 ◽  
Vol 950 ◽  
pp. 114865
Author(s):  
Jørgen Rasmussen
Keyword(s):  
Kac Modules

scholarly journals Complexity for modules over the classical Lie superalgebra

2012 ◽  
Vol 148 (5) ◽  
pp. 1561-1592 ◽  
Author(s):  
Brian D. Boe ◽  
Jonathan R. Kujawa ◽  
Daniel K. Nakano
Keyword(s):  
Lie Algebra ◽  
Lie Superalgebra ◽  
Projective Resolution ◽  
Lie Superalgebras ◽  
Simple Modules ◽  
Minimal Projective Resolution ◽  
Finite Dimensional ◽  
Reductive Lie Algebra ◽  
Completely Reducible ◽  
Kac Modules

AbstractLet ${\Xmathfrak g}={\Xmathfrak g}_{\zerox }\oplus {\Xmathfrak g}_{\onex }$ be a classical Lie superalgebra and let ℱ be the category of finite-dimensional ${\Xmathfrak g}$-supermodules which are completely reducible over the reductive Lie algebra ${\Xmathfrak g}_{\zerox }$. In [B. D. Boe, J. R. Kujawa and D. K. Nakano, Complexity and module varieties for classical Lie superalgebras, Int. Math. Res. Not. IMRN (2011), 696–724], we demonstrated that for any module M in ℱ the rate of growth of the minimal projective resolution (i.e. the complexity of M) is bounded by the dimension of ${\Xmathfrak g}_{\onex }$. In this paper we compute the complexity of the simple modules and the Kac modules for the Lie superalgebra $\Xmathfrak {gl}(m|n)$. In both cases we show that the complexity is related to the atypicality of the block containing the module.

scholarly journals Primitive vectors of Kac-modules of the Lie superalgebras sl(m/n)

2000 ◽  
Vol 41 (7) ◽  
pp. 5064-5087 ◽  
Author(s):  
Yucai Su ◽  
J. W. B. Hughes ◽  
R. C. King
Keyword(s):  
Lie Superalgebras ◽  
Kac Modules

Kac modules of sl (2/2) and the extended Kac‐Weyl formulas

Mathematika ◽  
1992 ◽  
Vol 39 (1) ◽  
pp. 37-48 ◽  
Author(s):  
H. Shakibi
Keyword(s):  
Kac Modules

scholarly journals Kazhdan–Lusztig equivalence and fusion of Kac modules in Virasoro logarithmic models

2012 ◽  
Vol 862 (1) ◽  
pp. 232-269 ◽  
Author(s):  
P.V. Bushlanov ◽  
A.M. Gainutdinov ◽  
I.Yu. Tipunin
Keyword(s):  
Kac Modules

On restricted representations of restricted contact Lie superalgebras of odd type

2016 ◽  
Vol 15 (04) ◽  
pp. 1650075 ◽  
Author(s):  
Shujuan Wang ◽  
Wende Liu
Keyword(s):  
Lie Superalgebras ◽  
Necessary Condition ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Kac Modules ◽  
Sufficient And Necessary Condition

Simple restricted modules are considered for the restricted contact Lie superalgebras of odd type over an algebraically closed field with characteristic [Formula: see text]. In particular, a sufficient and necessary condition in terms of typical or atypical weights is given for the restricted Kac modules to be simple. Furthermore, the number of the simple restricted Kac modules is obtained.

On the composition factors of Kac modules for the Lie superalgebras sl(m/n)

1992 ◽  
Vol 33 (2) ◽  
pp. 470-491 ◽  
Author(s):  
J. W. B. Hughes ◽  
R. C. King ◽  
J. Van der Jeugt
Keyword(s):  
Lie Superalgebras ◽  
Kac Modules ◽  
Composition Factors

Simplicity of Kac Modules for the Quantum General Linear Superalgebra

2019 ◽  
Vol 23 (4) ◽  
pp. 1737-1760
Author(s):  
Randall R. Holmes ◽  
Chaowen Zhang
Keyword(s):  
General Linear ◽  
Kac Modules
Sign in / Sign up

Export Citation Format

Share Document