Hilbert series, Howe duality, and branching rules
نویسندگان
چکیده
منابع مشابه
Hilbert series, Howe duality, and branching rules.
Let lambda be a partition, with l parts, and let F(lambda) be the irreducible finite dimensional representation of GL(m) associated to lambda when l < or = m. The Littlewood Restriction Rule describes how F(lambda) decomposes when restricted to the orthogonal group O(m) or to the symplectic group Sp(m2) under the condition that l < or = m2. In this paper, this result is extended to all partitio...
متن کاملHilbert Series and Gelfand Duality
Another example of such a duality are the formulas of Gelfand-Tsetlin for matrix elements of irreducible representations of the algebra of complex matrices with trace 0 and the formulas for coordinates in the group of unitary matrices... In all of these cases the duality consists in the fact that functions of discrete arguments satisfy finite difference equations analogous to differential equat...
متن کاملCategorical Geometric Skew Howe Duality
We categorify the R-matrix isomorphism between tensor products of minuscule representations of Uq(sln) by constructing an equivalence between the derived categories of coherent sheaves on the corresponding convolution products in the affine Grassmannian. The main step in the construction is a categorification of representations of Uq(sl2) which are related to representations of Uq(sln) by quant...
متن کاملHowe Duality for Lie Superalgebras
We study a dual pair of general linear Lie superalgebras in the sense of R. Howe. We give an explicit multiplicity-free decomposition of a symmetric and skew-symmetric algebra (in the super sense) under the action of the dual pair and present explicit formulas for the highest weight vectors in each isotypic subspace of the symmetric algebra. We give an explicit multiplicity-free decomposition i...
متن کاملThe Howe Duality and the Projective Representations of Symmetric Groups
The symmetric group Sk possesses a nontrivial central extension, whose irreducible representations, different from the irreducible representations of Sk itself, coincide with the irreducible representations of the algebra Ak generated by indeterminates τi,j for i 6= j, 1 ≤ i, j ≤ n subject to the relations τi,j = −τj,i, τ i,j = 1, τi,jτm,l = −τm,lτi,j if {i, j} ∩ {m, l} = ∅; τi,jτj,mτi,j = τj,m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 2003
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.0136632100