The Experts below are selected from a list of 267 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.
Yoshihiro Takeyama - One of the best experts on this subject based on the ideXlab platform.
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a Monomial Basis for the virasoro minimal series m p p the case 1 p p 2
Communications in Mathematical Physics, 2005Co-Authors: Boris Feigin, Tetsuji Miwa, M Jimbo, E Mukhin, Yoshihiro TakeyamaAbstract:Quadratic relations are given explicitly in two cases of chiral conformal field theory, and Monomial bases of the representation spaces are constructed by using the Fourier components of the intertwiners. The first case is the (2,1) primary fields for the (p,p′)-minimal series Mr,s (1≤r≤p−1,1≤s≤p′−1) for the Virasoro algebra where 1
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a Monomial Basis for the virasoro minimal series m p p the case 1 p p 2
arXiv: Quantum Algebra, 2004Co-Authors: Boris Feigin, Tetsuji Miwa, M Jimbo, E Mukhin, Yoshihiro TakeyamaAbstract:Quadratic relations of the intertwiners are given explicitly in two cases of chiral conformal field theory, and Monomial bases of the representation spaces are constructed by using the Fourier components of the intertwiners. The two cases are the (p,p')-minimal series for the Virasoro algebra where 1
Vanni Noferini - One of the best experts on this subject based on the ideXlab platform.
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structured backward errors in linearizations
arXiv: Numerical Analysis, 2019Co-Authors: Vanni Noferini, Leonardo Robol, Raf VandebrilAbstract:A standard approach to compute the roots of a univariate polynomial is to compute the eigenvalues of an associated confederate matrix instead, such as, for instance the companion or comrade matrix. The eigenvalues of the confederate matrix can be computed by Francis's QR algorithm. Unfortunately, even though the QR algorithm is provably backward stable, mapping the errors back to the original polynomial coefficients can still lead to huge errors. However, the latter statement assumes the use of a non-structure exploiting QR algorithm. In [J. Aurentz et al., Fast and backward stable computation of roots of polynomials, SIAM J. Matrix Anal. Appl., 36(3), 2015] it was shown that a structure exploiting QR algorithm for companion matrices leads to a structured backward error on the companion matrix. The proof relied on decomposing the error into two parts: a part related to the recurrence coefficients of the Basis (Monomial Basis in that case) and a part linked to the coefficients of the original polynomial. In this article we prove that the analysis can be extended to other classes of comrade matrices. We first provide an alternative backward stability proof in the Monomial Basis using structured QR algorithms; our new point of view shows more explicitly how a structured, decoupled error on the confederate matrix gets mapped to the associated polynomial coefficients. This insight reveals which properties must be preserved by a structure exploiting QR algorithm to end up with a backward stable algorithm. We will show that the previously formulated companion analysis fits in this framework and we will analyze in more detail Jacobi polynomials (Comrade matrices) and Chebyshev polynomials (Colleague matrices).
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on the stability of computing polynomial roots via confederate linearizations
IEEE Communications Magazine, 2015Co-Authors: Yuji Nakatsukasa, Vanni NoferiniAbstract:A common way of computing the roots of a polynomial is to nd the eigenvalues of a linearization, such as the companion (when the polynomial is expressed in the Monomial Basis), colleague (Chebyshev Basis) or comrade matrix (general orthogonal polynomial Basis). For the Monomial case, many studies exist on the stability of linearization-based rootnding algorithms. By contrast, little seems to be known for other polynomial bases. This paper studies the stability of algorithms that compute the roots via linearization in nonMonomial bases, and has three goals. First we prove its normwise stability when the polynomial is properly scaled and the QZ algorithm (as opposed to the more commonly used QR algorithm) is applied to a comrade pencil associated with a Jacobi orthogonal polynomial. Second, we extend a result by Arnold that leads to a rst-order expansion of the backward error when the eigenvalues are computed via QR, which shows that the method can be unstable. Finally, we focus on the special case of Chebyshev Basis, in particular the Chebfun rootnder: we discuss its stability and describe an optional functionality, made available for improved stability, for computing the roots of a general continuous function f(x), implemented in the recently updated version 5. The main message is that to guarantee backward stability QZ applied to a properly scaled pencil is necessary
Boris Feigin - One of the best experts on this subject based on the ideXlab platform.
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a Monomial Basis for the virasoro minimal series m p p the case 1 p p 2
Communications in Mathematical Physics, 2005Co-Authors: Boris Feigin, Tetsuji Miwa, M Jimbo, E Mukhin, Yoshihiro TakeyamaAbstract:Quadratic relations are given explicitly in two cases of chiral conformal field theory, and Monomial bases of the representation spaces are constructed by using the Fourier components of the intertwiners. The first case is the (2,1) primary fields for the (p,p′)-minimal series Mr,s (1≤r≤p−1,1≤s≤p′−1) for the Virasoro algebra where 1
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a Monomial Basis for the virasoro minimal series m p p the case 1 p p 2
arXiv: Quantum Algebra, 2004Co-Authors: Boris Feigin, Tetsuji Miwa, M Jimbo, E Mukhin, Yoshihiro TakeyamaAbstract:Quadratic relations of the intertwiners are given explicitly in two cases of chiral conformal field theory, and Monomial bases of the representation spaces are constructed by using the Fourier components of the intertwiners. The two cases are the (p,p')-minimal series for the Virasoro algebra where 1
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vertex operator algebra arising from the minimal series m 3 p and Monomial Basis
arXiv: Quantum Algebra, 2002Co-Authors: Boris Feigin, Michio Jimbo, Tetsuji MiwaAbstract:We study a vertex operator algebra (VOA)Vrelated to the M(3, p) Virasoro minimal series. This VOA reduces in the simplest case p = 4 to the level-two integrable vacuum module of \({\widehat {sl}_2}\). On V there is an action of a commutative current a(z), which is an analog of the current e(z) of \({\widehat {sl}_2}\). Our main concern is the subspace W generated by this action from the highest weight vector of V. Using the Fourier components of a(z), we present a Monomial Basis of W and a semi-infinite Monomial Basis of V. We also give a Gordon type formula for their characters.