scholarly journals The Kac–Wakimoto character formula for the general linear Lie superalgebra

2015 ◽  
Vol 9 (6) ◽  
pp. 1419-1452 ◽  
Author(s):  
Michael Chmutov ◽  
Crystal Hoyt ◽  
Shifra Reif
Keyword(s):  
Lie Superalgebra ◽  
Character Formula ◽  
General Linear ◽  
General Linear Lie Superalgebra

Double Derivations of n-Lie Superalgebras

2018 ◽  
Vol 25 (01) ◽  
pp. 161-180
Author(s):  
Bing Sun ◽  
Liangyun Chen ◽  
Xin Zhou
Keyword(s):  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
General Linear ◽  
Base Field ◽  
Inner Derivation ◽  
Derivation Algebra ◽  
General Linear Lie Superalgebra

Let 𝔤 be an n-Lie superalgebra. We study the double derivation algebra [Formula: see text] and describe the relation between [Formula: see text] and the usual derivation Lie superalgebra Der(𝔤). We show that the set [Formula: see text] of all double derivations is a subalgebra of the general linear Lie superalgebra gl(𝔤) and the inner derivation algebra ad(𝔤) is an ideal of [Formula: see text]. We also show that if 𝔤 is a perfect n-Lie superalgebra with certain constraints on the base field, then the centralizer of ad(𝔤) in [Formula: see text] is trivial. Finally, we give that for every perfect n-Lie superalgebra 𝔤, the triple derivations of the derivation algebra Der(𝔤) are exactly the derivations of Der(𝔤).

scholarly journals The Z2×Z2-graded general linear Lie superalgebra

2020 ◽  
Vol 61 (1) ◽  
pp. 011702
Author(s):  
Phillip S. Isaac ◽  
N. I. Stoilova ◽  
Joris Van der Jeugt
Keyword(s):  
Lie Superalgebra ◽  
General Linear ◽  
General Linear Lie Superalgebra

scholarly journals Super tableaux and a branching rule for the general linear Lie superalgebra

2014 ◽  
Vol 63 (2) ◽  
pp. 274-282 ◽  
Author(s):  
Sean Clark ◽  
Yung-Ning Peng ◽  
S. Kuang Thamrongpairoj
Keyword(s):  
Lie Superalgebra ◽  
General Linear ◽  
Branching Rule ◽  
General Linear Lie Superalgebra

scholarly journals Equivalence of Blocks for the General Linear Lie Superalgebra

2013 ◽  
Vol 103 (12) ◽  
pp. 1313-1327 ◽  
Author(s):  
Shun-Jen Cheng ◽  
Volodymyr Mazorchuk ◽  
Weiqiang Wang
Keyword(s):  
Lie Superalgebra ◽  
General Linear ◽  
General Linear Lie Superalgebra

scholarly journals Yangian of the General Linear Lie Superalgebra

2020 ◽  
Author(s):  
Maxim Nazarov ◽  
Keyword(s):  
Lie Superalgebra ◽  
General Linear ◽  
Basic Properties ◽  
General Linear Lie Superalgebra

We prove several basic properties of the Yangian of the Lie superalgebra gl(M|N).

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
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