Extensions Between Generalized Verma Modules: The Hermitian Symmetric Cases.

Brad Shelton

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Following the work of Daniel Barlet [Pitman Res. Notes Math. Ser. 366 (1997), 19-59] and Ridha Belgrade [J. Algebra 245 (2001), 193-224], the aim of this article is to study the existence of (a,b)-hermitian forms on regular (a,b)-modules. We show that every regular (a,b)-module E with a non-degenerate bilinear form can be written in a unique way as a direct sum of (a,b)-modules $E_{i}$ that admit either an (a,b)-hermitian or an (a,b)-anti-hermitian form or both; all three cases are possible,...