scholarly journals Tensor product categorifications, Verma modules and the blob 2-category

2021 ◽  
Author(s):  
Abel Lacabanne ◽  
Grégoire Naisse ◽  
Pedro Vaz
Keyword(s):  
Tensor Product ◽  
Verma Modules

scholarly journals Highest-weight vectors in tensor products of Verma modules for U_q(sl_2)

2018 ◽  
Vol 36 (4) ◽  
pp. 107-119 ◽  
Author(s):  
Elizabeth Creath ◽  
Dijana Jakelic
Keyword(s):  
Tensor Product ◽  
Tensor Products ◽  
Alternative Proof ◽  
Verma Modules ◽  
Direct Sums ◽  
Indecomposable Modules ◽  
Enveloping Algebra ◽  
Highest Weight ◽  
Structure Constants ◽  
Quantized Universal Enveloping Algebra

We obtain an explicit basis for the subspace spanned by highest-weight vectors in a tensor product of two highest-weight modules for the quantized universal enveloping algebra of sl_2. The structure constants provide a generalization of the Clebsh-Gordan coefficients. As a byproduct, we give an alternative proof for the decomposition of these tensor products as direct sums of indecomposable modules and supply generators for all highest weight summands.

scholarly journals GENERALIZED GAUSS DECOMPOSITION OF TRIGONOMETRIC R-MATRICES

1995 ◽  
Vol 10 (19) ◽  
pp. 1375-1392 ◽  
Author(s):  
S.M. KHOROSHKIN ◽  
A.A. STOLIN ◽  
V.N. TOLSTOY
Keyword(s):  
Tensor Product ◽  
Bilinear Form ◽  
Central Charge ◽  
Irreducible Representations ◽  
Verma Modules ◽  
R Matrix ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Gauss Decomposition ◽  
Affine Algebras

The general formula for the universal R-matrix for quantized nontwisted affine algebras, obtained by the first and third authors, is applied to zero central charge, highest weight modules of the quantized affine algebras. It is shown how the universal R-matrix produces the Gauss decomposition of trigonometric R-matrix in tensor product of these modules. In particular, [Formula: see text] current realization of the universal R-matrix is presented. It gives a new universal presentation for the trigonometric R-matrix with a parameter in tensor product of Uq(sl2)-Verma modules. Detailed analysis of a scalar factor arising in finite-dimensional representations of the universal R-matrix for any Uq(ĝ) is given. We interpret this scalar factor as a multiplicative bilinear form on highest weight polynomials of irreducible representations and express this form in terms of infinite q-shifted factorials.

Reference Signal Based Tensor Product Expansion for EOG-Related Artifact Separation in EEG

2017 ◽  
Vol E100.A (11) ◽  
pp. 2230-2237
Author(s):  
Akitoshi ITAI ◽  
Arao FUNASE ◽  
Andrzej CICHOCKI ◽  
Hiroshi YASUKAWA
Keyword(s):  
Tensor Product ◽  
Reference Signal

On degeneracy problem of NFSRs via semi-tensor product

2020 ◽  
Author(s):  
Xinyu Zhao ◽  
Biao Wang ◽  
Shuqian Zhu ◽  
Jun-e Feng
Keyword(s):  
Tensor Product ◽  
Degeneracy Problem

On the Buchstaber Subring in MSp∗

1998 ◽  
Vol 5 (5) ◽  
pp. 401-414
Author(s):  
M. Bakuradze
Keyword(s):  
Tensor Product ◽  
Characteristic Classes ◽  
Generalized Quaternion ◽  
Symplectic Cobordisms

Abstract A formula is given to calculate the last n number of symplectic characteristic classes of the tensor product of the vector Spin(3)- and Sp(n)-bundles through its first 2n number of characteristic classes and through characteristic classes of Sp(n)-bundle. An application of this formula is given in symplectic cobordisms and in rings of symplectic cobordisms of generalized quaternion groups.

scholarly journals Fractal Frames of Functions on the Rectangle

2021 ◽  
Vol 5 (2) ◽  
pp. 42
Author(s):  
María A. Navascués ◽  
Ram Mohapatra ◽  
Md. Nasim Akhtar
Keyword(s):  
Tensor Product ◽  
Product Space ◽  
Integrable Function ◽  
Two Dimensional ◽  
Tensor Product Space ◽  
Fractal Functions

In this paper, we define fractal bases and fractal frames of L2(I×J), where I and J are real compact intervals, in order to approximate two-dimensional square-integrable maps whose domain is a rectangle, using the identification of L2(I×J) with the tensor product space L2(I)⨂L2(J). First, we recall the procedure of constructing a fractal perturbation of a continuous or integrable function. Then, we define fractal frames and bases of L2(I×J) composed of product of such fractal functions. We also obtain weaker families as Bessel, Riesz and Schauder sequences for the same space. Additionally, we study some properties of the tensor product of the fractal operators associated with the maps corresponding to each variable.

scholarly journals Classification of Degenerate Verma Modules for E(5, 10)

2021 ◽  
Author(s):  
Nicoletta Cantarini ◽  
Fabrizio Caselli ◽  
Victor Kac
Keyword(s):  
Infinite Number ◽  
Verma Module ◽  
Lie Superalgebra ◽  
Verma Modules ◽  
Singular Vectors ◽  
Finite Dimensional ◽  
De Rham ◽  
Via Classification

AbstractGiven a Lie superalgebra $${\mathfrak {g}}$$ g with a subalgebra $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 , and a finite-dimensional irreducible $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 -module F, the induced $${\mathfrak {g}}$$ g -module $$M(F)={\mathcal {U}}({\mathfrak {g}})\otimes _{{\mathcal {U}}({\mathfrak {g}}_{\ge 0})}F$$ M ( F ) = U ( g ) ⊗ U ( g ≥ 0 ) F is called a finite Verma module. In the present paper we classify the non-irreducible finite Verma modules over the largest exceptional linearly compact Lie superalgebra $${\mathfrak {g}}=E(5,10)$$ g = E ( 5 , 10 ) with the subalgebra $${\mathfrak {g}}_{\ge 0}$$ g ≥ 0 of minimal codimension. This is done via classification of all singular vectors in the modules M(F). Besides known singular vectors of degree 1,2,3,4 and 5, we discover two new singular vectors, of degrees 7 and 11. We show that the corresponding morphisms of finite Verma modules of degree 1,4,7, and 11 can be arranged in an infinite number of bilateral infinite complexes, which may be viewed as “exceptional” de Rham complexes for E(5, 10).

Combining improved genetic algorithm and matrix semi-tensor product (STP) in color image encryption

2021 ◽  
Vol 183 ◽  
pp. 108041
Author(s):  
Xiuli Chai ◽  
Xiangcheng Zhi ◽  
Zhihua Gan ◽  
Yushu Zhang ◽  
Yiran Chen ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Tensor Product ◽  
Image Encryption ◽  
Color Image ◽  
Improved Genetic Algorithm ◽  
Color Image Encryption
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