• Title/Summary/Keyword: tensor product representation

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REPRESENTATIONS FOR LIE SUPERALGEBRA spo(2m,1)

  • Lee, Chan-Young
    • Journal of the Korean Mathematical Society
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    • v.36 no.3
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    • pp.593-607
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    • 1999
  • Let denote the orthosymplectic Lie superalgebra spo (2m,1). For each irreducible -module, we describe its character in terms of tableaux. Using this result, we decompose kV, the k-fold tensor product of the natural representation V of , into its irreducible -submodules, and prove that the Brauer algebra Bk(1-2m) is isomorphic to the centralizer algebra of spo(2m, 1) on kV for m .

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HIGHEST WEIGHT VECTORS OF IRREDUCIBLE REPRESENTATIONS OF THE QUANTUM SUPERALGEBRA μq(gl(m, n))

  • Moon, Dong-Ho
    • Journal of the Korean Mathematical Society
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    • v.40 no.1
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    • pp.1-28
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    • 2003
  • The Iwahori-Hecke algebra $H_{k}$ ( $q^2$) of type A acts on the k-fold tensor product space of the natural representation of the quantum superalgebra (equation omitted)$_{q}$(gl(m, n)). We show the Hecke algebra $H_{k}$ ( $q^2$) and the quantum superalgebra (equation omitted)$_{q}$(gl(m n)) have commuting actions on the tensor product space, and determine the centralizer of each other. Using this result together with Gyoja's q-analogue of the Young symmetrizers, we construct highest weight vectors of irreducible summands of the tensor product space.

On the Tensor Product of m-Partition Algebras

  • Kennedy, A. Joseph;Jaish, P.
    • Kyungpook Mathematical Journal
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    • v.61 no.4
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    • pp.679-710
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    • 2021
  • We study the tensor product algebra Pk(x1) ⊗ Pk(x2) ⊗ ⋯ ⊗ Pk(xm), where Pk(x) is the partition algebra defined by Jones and Martin. We discuss the centralizer of this algebra and corresponding Schur-Weyl dualities and also index the inequivalent irreducible representations of the algebra Pk(x1) ⊗ Pk(x2) ⊗ ⋯ ⊗ Pk(xm) and compute their dimensions in the semisimple case. In addition, we describe the Bratteli diagrams and branching rules. Along with that, we have also constructed the RS correspondence for the tensor product of m-partition algebras which gives the bijection between the set of tensor product of m-partition diagram of Pk(n1) ⊗ Pk(n2) ⊗ ⋯ ⊗ Pk(nm) and the pairs of m-vacillating tableaux of shape [λ] ∈ Γkm, Γkm = {[λ] = (λ1, λ2, …, λm)|λi ∈ Γk, i ∈ {1, 2, …, m}} where Γk = {λi ⊢ t|0 ≤ t ≤ k}. Also, we provide proof of the identity $(n_1n_2{\cdots}n_m)^k={\sum}_{[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$ f[λ]mk[λ] where mk[λ] is the multiplicity of the irreducible representation of $S{_{n_1}}{\times}S{_{n_2}}{\times}....{\times}S{_{n_m}}$ module indexed by ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$, where f[λ] is the degree of the corresponding representation indexed by ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$ and ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}=\{[{\lambda}]=({\lambda}_1,{\lambda}_2,{\ldots},{\lambda}_m){\mid}{\lambda}_i{\in}{\Lambda}^k_{n_i},i{\in}\{1,2,{\ldots},m\}\}$ where ${\Lambda}^k_{n_i}=\{{\mu}=({\mu}_1,{\mu}_2,{\ldots},{\mu}_t){\vdash}n_i{\mid}n_i-{\mu}_1{\leq}k\}$.

REPRESENTATIONS OF THE BRAID GROUP $B_4$

  • Lee, Woo
    • Journal of the Korean Mathematical Society
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    • v.34 no.3
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    • pp.673-693
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    • 1997
  • In this work, the irreducible complex representations of degree 4 of $B_4$, the braid group on 4 strings, are classified. There are 4 families of representations: A two-parameter family of representations for which the image of $P_4$, the pure braid group on 4 strings, is abelian; two families of representations which are the composition of an irreducible representation of $B_3$, the braid group on 3 strings, with a certain special homomorphism $\pi : B_4 \longrightarrow B_3$; a family of representations which are the tensor product of 2 irreducible two-dimensional representations of $B_4$.

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Shell Finite Element Based on B-Spline Representation for Finite Rotations (B-Spline 곡면 모델링을 이용한 기하비선형 쉘 유한요소)

  • 노희열;조맹효
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2003.10a
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    • pp.429-436
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    • 2003
  • A new linkage framework between elastic shell element with finite rotation and computar-aided geometric design (CAGD) (or surface is developed in the present study. The framework of shell finite element is based on the generalized curved two-parametric coordinate system. To represent free-form surface, cubic B-spline tensor-product functions are used. Thus the present finite element can be directly linked into the geometric modeling produced by surface generation tool in CAD software. The efficiency and accuracy of the Previously developed linear elements hold for the nonlinear element with finite rotations. To handle the finite rotation behavior of shells, exponential mapping in the SO(3) group is employed to allow the large incremental step size. The integrated frameworks of shell geometric design and nonlinear computational analysis can serve as an efficient tool in shape and topological design of surfaces with large deformations.

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