Abstract
If p is an arbitrary parabolic subsuperalgebra of g = gl(m + nɛ), p(m), a character formula for the generic finite-dimensional irreducible g-module, such that p is the stabilizer of its lowest weight space, is announced. Furthermore, an estimate for the character of any finite-dimensional irreducible g-module in terms of its highest weight with respect to a distinguished Borel subsuperalgebra is presented (inequality (4)) and a sufficient condition for this to be an equality is found. In this way, two generalizations of the Kac character formula for typical modules are obtained: a formula concerning an arbitrary Borel subsuperalgebra ((1)) and a more effective formula ((3)) for the special case of a distinguished Borel subsuperalgebra. The complete proofs will appear in [14].
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Partially supported by Contract 911/11.04.88 with the Bulgarian Ministry of Culture, Science, and Education.
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Penkov, I., Serganova, V. Character formulas for some classes of atypical gl(m+nε)- and p(m)-modules. Lett Math Phys 16, 251–261 (1988). https://doi.org/10.1007/BF00398962
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DOI: https://doi.org/10.1007/BF00398962