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Character formulas for some classes of atypical gl(m+nε)- andp(m)-modules

✍ Scribed by Ivan Penkov; Vera Serganova


Publisher
Springer
Year
1988
Tongue
English
Weight
416 KB
Volume
16
Category
Article
ISSN
0377-9017

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✦ Synopsis


Ifp is an arbitrary parabolic suhsuperalgebra of 9 = gl(m + ns), 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 B orel subsuperalgebra. The complete proofs will appear in [14].