The Experts below are selected from a list of 21564 Experts worldwide ranked by ideXlab platform
Oded Yacobi - One of the best experts on this subject based on the ideXlab platform.
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a basis for the Symplectic Group branching algebra
Journal of Algebraic Combinatorics, 2012Co-Authors: Sangjib Kim, Oded YacobiAbstract:The Symplectic Group branching algebra, $\mathcal {B}$ , is a graded algebra whose components encode the multiplicities of irreducible representations of Sp2n?2(?) in each finite-dimensional irreducible representation of Sp2n (?). By describing on $\mathcal {B}$ an ASL structure, we construct an explicit standard monomial basis of $\mathcal {B}$ consisting of Sp2n?2(?) highest weight vectors. Moreover, $\mathcal {B}$ is known to carry a canonical action of the n-fold product SL2×?×SL2, and we show that the standard monomial basis is the unique (up to scalar) weight basis associated to this representation. Finally, using the theory of Hibi algebras we describe a deformation of $\mathrm{Spec}(\mathcal {B})$ into an explicitly described toric variety.
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a basis for the Symplectic Group branching algebra
arXiv: Representation Theory, 2010Co-Authors: Sangjib Kim, Oded YacobiAbstract:The Symplectic Group branching algebra, B, is a graded algebra whose components encode the multiplicities of irreducible representations of Sp(2n-2,C) in each irreducible representation of Sp(2n,C). By describing on B an ASL structure, we construct an explicit standard monomial basis of B consisting of Sp(2n-2,C) highest weight vectors. Moreover, B is known to carry a canonical action of the n-fold product SL(2) \times ... \times SL(2), and we show that the standard monomial basis is the unique (up to scalar) weight basis associated to this representation. Finally, using the theory of Hibi algebras we describe a deformation of Spec(B) into an explicit toric variety.
Sangjib Kim - One of the best experts on this subject based on the ideXlab platform.
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a basis for the Symplectic Group branching algebra
Journal of Algebraic Combinatorics, 2012Co-Authors: Sangjib Kim, Oded YacobiAbstract:The Symplectic Group branching algebra, $\mathcal {B}$ , is a graded algebra whose components encode the multiplicities of irreducible representations of Sp2n?2(?) in each finite-dimensional irreducible representation of Sp2n (?). By describing on $\mathcal {B}$ an ASL structure, we construct an explicit standard monomial basis of $\mathcal {B}$ consisting of Sp2n?2(?) highest weight vectors. Moreover, $\mathcal {B}$ is known to carry a canonical action of the n-fold product SL2×?×SL2, and we show that the standard monomial basis is the unique (up to scalar) weight basis associated to this representation. Finally, using the theory of Hibi algebras we describe a deformation of $\mathrm{Spec}(\mathcal {B})$ into an explicitly described toric variety.
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a basis for the Symplectic Group branching algebra
arXiv: Representation Theory, 2010Co-Authors: Sangjib Kim, Oded YacobiAbstract:The Symplectic Group branching algebra, B, is a graded algebra whose components encode the multiplicities of irreducible representations of Sp(2n-2,C) in each irreducible representation of Sp(2n,C). By describing on B an ASL structure, we construct an explicit standard monomial basis of B consisting of Sp(2n-2,C) highest weight vectors. Moreover, B is known to carry a canonical action of the n-fold product SL(2) \times ... \times SL(2), and we show that the standard monomial basis is the unique (up to scalar) weight basis associated to this representation. Finally, using the theory of Hibi algebras we describe a deformation of Spec(B) into an explicit toric variety.
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The nullcone in the multi-vector representation of the Symplectic Group and related combinatorics
arXiv: Representation Theory, 2009Co-Authors: Sangjib KimAbstract:We study the nullcone in the multi-vector representation of the Symplectic Group with respect to a joint action of the general linear Group and the Symplectic Group. By extracting an algebra over a distributive lattice structure from the coordinate ring of the nullcone, we describe a toric degeneration and standard monomial theory of the nullcone in terms of double tableaux and integral points in a convex polyhedral cone.
Vladimír Souček - One of the best experts on this subject based on the ideXlab platform.
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Fischer decomposition for the Symplectic Group
Journal of Mathematical Analysis and Applications, 2018Co-Authors: Fred Brackx, H. De Schepper, David Eelbode, Roman Lávička, Vladimír SoučekAbstract:We prove the Fischer decomposition for the space of spinor-valued polynomials, defined on Euclidean space of four-fold dimension, in terms of irreducible modules for the Symplectic Group, consisting of so-called osp(4|2)-monogenics.
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A reciprocity law and the skew Pieri rule for the Symplectic Group
Journal of Mathematical Physics, 2017Co-Authors: Roger Howe, Roman Lávička, Soo Teck Lee, Vladimír SoučekAbstract:We use the theory of skew duality to show that decomposing the tensor product of k irreducible representations of the Symplectic Group Sp2m=Sp2m(ℂ) is equivalent to branching from Sp2n to Sp2n1×⋯×Sp2nk, where n,n1,…,nk are positive integers such that n=n1+⋯+nk and the njs depend on m as well as the representations in the tensor product. Using this result and a work of Lepowsky, we obtain a skew Pieri rule for Sp2m, i.e., a description of the irreducible decomposition of the tensor product of an irreducible representation of the Symplectic Group Sp2m with a fundamental representation.
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A reciprocity law and the skew Pieri rule for the Symplectic Group
arXiv: Representation Theory, 2016Co-Authors: Roger Howe, Roman Lávička, Soo Teck Lee, Vladimír SoučekAbstract:We use the theory of skew duality to show that decomposing the tensor product of $k$ irreducible representations of the Symplectic Group $Sp_{2m} = Sp_{2m}(C)$ is equivalent to branching from $Sp_{2n}$ to $Sp_{2n_1}\times\cdots\times Sp_{2n_k}$ where $n, n_1,\ldots, n_k$ are positive integers such that $n = n_1+\cdots+n_k$ and the $n_j$'s depend on $m$ as well as the representations in the tensor product. Using this result and a work of J. Lepowsky, we obtain a skew Pieri rule for $Sp_{2m}$, i.e., a description of the irreducible decomposition of the tensor product of an irreducible representation of the Symplectic Group $Sp_{2m}$ with a fundamental representation.
Piotr śniady - One of the best experts on this subject based on the ideXlab platform.
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integration with respect to the haar measure on unitary orthogonal and Symplectic Group
Communications in Mathematical Physics, 2006Co-Authors: Benoit Collins, Piotr śniadyAbstract:We revisit the work of the first named author and using simpler algebraic arguments we calculate integrals of polynomial functions with respect to the Haar measure on the unitary Group U(d). The previous result provided exact formulas only for 2d bigger than the degree of the integrated polynomial and we show that these formulas remain valid for all values of d. Also, we consider the integrals of polynomial functions on the orthogonal Group O(d) and the Symplectic Group Sp(d). We obtain an exact character expansion and the asymptotic behavior for large d. Thus we can show the asymptotic freeness of Haar-distributed orthogonal and Symplectic random matrices, as well as the convergence of integrals of the Itzykson–Zuber type.
Arik Wilbert - One of the best experts on this subject based on the ideXlab platform.
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topology of two row springer fibers for the even orthogonal and Symplectic Group
arXiv: Representation Theory, 2015Co-Authors: Arik WilbertAbstract:We construct an explicit topological model (similar to the topological Springer fibers appearing in work of Khovanov and Russell) for every two-row Springer fiber associated with the even orthogonal Group and prove that the respective topological model is homeomorphic to its corresponding Springer fiber. This confirms a conjecture by Ehrig and Stroppel concerning the topology of the equal-row Springer fiber for the even orthogonal Group. Moreover, we show that every two-row Springer fiber for the Symplectic Group is homeomorphic (even isomorphic as an algebraic variety) to a connected component of a certain two-row Springer fiber for the even orthogonal Group.
