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CiteSeerX-Kazhdan-Lusztig polynomials for hermitian symmetric. was shown for the classical Hermitian symmetric cases that these sets of roots. analyze the categories of highest weight modules with a semiregular general-Highest weight modules, Verma modules, Hermitian symmetric pairs,.. Categories of highest weight modules: Applications to classical Hermitian symmetric. Highest weight modules for Hermitian symmetric pairs of exceptional. Multiplicity-free Theorems of the Restrictions of Unitary Highest. highest weight categories arising from khovanov's diagram algebra i Finite-dimensional algebras and highest weight categories, J. reine angew. Math. 44 T J Enright and B Shelton, Categories of highest weight modules: applications to classical. Hermitian symmetric pairs, Memoirs AMS 67 1987, no. 367. Vitae-Franklin College Faculty-University of Georgia Filtrations on generalized Verma modules for Hermitian symmetric pairs. Categories of highest weight modules: applications to classical Hermitian symmetric Compressed PostScript file-European Mathematical Society The complex analytic methods have found a wide range of applications in the study. of restricting highest weight modules with respect to reductive symmetric pairs. the Plancherel theorem for Hermitian symmetric spaces also for line bundle multiplicity-free representation branching rule symmetric pair highest weight Highest Weight Modules for Hermitian Symmetric Pairs of.-JStor Quasi-hereditary algebras and highest weight categories play an important role in representation. which again comes along with three distinguished classes of modules. Cellular algebras. application of the results about GLmn from Part IV see BS for details Choose a symmetric pair of a cup and a cap in the. Title, Categories of Highest Weight Modules: Applications to Classical Hermitian Symmetric Pairs Volume 367 of American Mathematical Society: Memoirs of the. Bibliography 7 T. J. Enright and B. Shelton, Categories of highest weight modules: applications to classical Hermitian symmetric pairs, to appear in Mem.Amer. Math. Soc. Full Text PDF Publication » Categories of highest weight modules: applications to classical Hermitian symmetric pairs / Thomas J. Enright and Brad Shelton. Multiplicity-free theorems of the restrictions of unitary highest weight. irreducible Hermitian symmetric pair G,K with integral highest weights Categories of highest weight modules: applications to classical Hermitian symmetric Representation Theory of Lie Groups-IMS Highest weight modules for Hermitian symmetric pairs of exceptional type. Categories of highest weight modules: applications to classical Hermitian symmetric For screen-MSP 1987, English, Book, Illustrated edition: Categories of highest weight modules: applications to classical Hermitian symmetric pairs / Thomas J. Enright and Brad Categories of Highest Weight Modules: Applications to Classical. Amazon.co.jp? Categories of Highest Weight Modules: Applications to Classical Hermitian Symmetric Pairs Memoirs of the American Mathematical Society: Boe,...

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An extension of the Littlewood Restriction Rule is given that covers all pertinent parameters and simplifies to the original under Littlewood's hypotheses. Two formulas are derived for the Gelfand-Kirillov dimension of any unitary highest weight representation occurring in a dual pair setting, one in terms of the dual pair index and the other in terms of the highest weight. For a fixed dual pair setting, all the irreducible highest weight representations which occur have the same Gelfand-Kirillov dimension.We define a class of unitary highest weight representations and show that each of these representations, L, has a Hilbert series H L (q) of the form:where R(q) is an explictly given multiple of the Hilbert series of a finite dimensional representation B of a real Lie algebra associated to L. Under this correspondence L → B , the two components of the Weil representation of the symplectic group correspond to the two spin representations of an orthogonal group.