Chapter 5. Irreducible representations of Lie superalgebras

1992 ◽  
Keyword(s):  
Lie Superalgebras ◽  
Irreducible Representations

scholarly journals GENERIC IRREDUCIBLE REPRESENTATIONS OF FINITE-DIMENSIONAL LIE SUPERALGEBRAS

1994 ◽  
Vol 05 (03) ◽  
pp. 389-419 ◽  
Author(s):  
IVAN PENKOV ◽  
VERA SERGANOVA
Keyword(s):  
Irreducible Module ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Irreducible Representations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Finite Dimensionality ◽  
Necessary And Sufficient

A theory of highest weight modules over an arbitrary finite-dimensional Lie superalgebra is constructed. A necessary and sufficient condition for the finite-dimensionality of such modules is proved. Generic finite-dimensional irreducible representations are defined and an explicit character formula for such representations is written down. It is conjectured that this formula applies to any generic finite-dimensional irreducible module over any finite-dimensional Lie superalgebra. The conjecture is proved for several classes of Lie superalgebras, in particular for all solvable ones, for all simple ones, and for certain semi-simple ones.

scholarly journals Polynomial identities for simple Lie superalgebras

1987 ◽  
Vol 28 (3) ◽  
pp. 310-327 ◽  
Author(s):  
M. D. Gould
Keyword(s):  
Tensor Product ◽  
Lie Superalgebra ◽  
Weight Vector ◽  
Lie Superalgebras ◽  
Irreducible Representations ◽  
Polynomial Identities ◽  
Minimal Weight ◽  
Finite Dimensional ◽  
Basic Classical Lie Superalgebra

AbstractPolynomial identities for the generators of a simple basic classical Lie superalgebra are derived in arbitrary representations generated by a maximal (or minimal) weight vector. The infinitesimal characters occurring in the tensor product of two finite dimensional irreducible representations are also determined.

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