• Kyungpook Mathematical Journal
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• v.45 no.3
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• pp.303-338
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• 2005

In this paper, we study unitary representations of the group $GL(n,{\mathbb{R}}){\ltimes}{\mathbb{R}}^{(m,n)}$.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.521-529
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• 1994

This paper studies the realization of irreducible unitary representations of $GL_2(R)$ and $GL_2(C)$ by Bargmann's classification[1]. Since the representations of general matrix groups can be obtained by the extensions of characters of a special linear group, we shall follow to a large extent the pattern of the results in [5], [6], and [8]. This article is divided into two sections. In the first section we describe the realization of principal series and discrete series and complementary series of $GL_2(R)$. The last section is devoted to the derivation of principal series and complementary series of $GL_2(C).

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.128-128
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• 1985

• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.831-867
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• 2003

In this paper, we find the unitary dual of the group SL(2,R)(equation omitted)R($^{m,2}$) and study automorphic forms related to the group SL(2,R)(equation omitted)R($^{m, 2}$).).

• Honam Mathematical Journal
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• v.6 no.1
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• pp.59-83
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• 1984

• Journal of the Korean Mathematical Society
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• v.31 no.1
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• pp.139-148
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• 1994

• Honam Mathematical Journal
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• v.8 no.1
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• pp.95-114
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• 1986

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.7-14
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• 2009

In this short note, we consider a family of linear representations of the braid group and the fundamental group of a punctured torus bundle over the circle. We construct an irreducible (special) unitary representation of the fundamental group of a closed 3-manifold obtained by the Dehn filling.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.3
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• pp.267-282
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• 2019

This paper examines how one can build a block tridiagonal structure for k-almost normal matrices and also for k-almost conjugate normal matrices. We shall see that these representations are created by unitary similarity and unitary congruance transformations, respectively. It shall be proven that the orders of diagonal blocks are 1, k + 2, 2k + 3, ${\ldots}$, in both cases. Then these block tridiagonal structures shall be reviewed for the cases where the mentioned matrices satisfy in a second-degree polynomial. Finally, for these processes, algorithms are presented.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.471-478
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• 2002

Let $Let\eta={\eta m}m$ be an eventually constant sequence of unit vectors $\eta m$ in $C^{n}$ and let $\rho$η be the pure state on $UHF_{n}$ algebra which is defined by $\rho\eta(\upsilon_i_1....\upsilon_i_k{\upsilon_{j1}}^*...{\upsilon_{j1}}^*)={\eta_1}^{i1}...{\eta_k}^{ik}{\eta_k}^{jk}...{\eta_1}^{j1}$. We find infinitely many state extensions of $\rho\eta$ to Cuntz algebra $O_n$ using representations and unitary operators. Also, we present theirconcrete expressions.