• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1893-1908
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• 2016

In this paper, we obtain some behaviours of theta sums of higher index for the $Schr{\ddot{o}}dinger$-Weil representation of the Jacobi group associated with a positive definite symmetric real matrix of degree m.

• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.525-542
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• 2002

In this article, we prove a certain local-global principle for representation of binary forms by an infinite family of quinary positive integral quadratic forms.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.17-25
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• 2006

In this paper, we study the right regular representation $R_\Gamma$ of a finite group G on the vector space consisting of vector valued functions on ${\Gamma}/G$ with a subgroup r of G and give a trace formula using the work of M. -F. Vigneras.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.345-370
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• 1997

In this paper, we introduce the Fock representation $U^{F, M}$ of the Heisenberg group $H_R^(g, h)$ associated with a positive definite symmetric half-integral matrix $M$ of degree h and prove that $U^{F, M}$ is unitarily equivalent to the Schrodinger representation of index $M$.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.41-55
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• 1992

The characteristic free representation theory of the general linear group is one of the powerful tools in the study of invariant theory, algebraic geometry, and commutative algebra. Recently the study of such representations became a popular theme. In this paper we study the representation-theoretic structures of the symmetric algebra and the exterior algebra over a commutative ring with unity 1.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.287-296
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• 2007

Using the representation of the solution by means of the resolvent, we study the boundedness of the solutions of some Volterra difference equations.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.2
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• pp.131-143
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• 2005

We give bibasic expansion for basic Appell functions ${\Phi}^{(1)}$ and ${\Phi}^{(2)}$, and their integral representations. We also give a continued fraction representation for ${\Phi}^{(2)}$.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.487-498
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• 2007

In this paper, we obtain important combinatorial identities of generalized harmonic numbers using symmetric polynomials. We also obtain the matrix representation for the generalized harmonic numbers whose inverse matrix can be computed recursively.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1497-1522
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• 2023

In this paper we compute the Bredon homology of wallpaper groups with respect to the family of finite groups and with coefficients in the complex representation ring. We provide explicit bases of the homology groups in terms of irreducible characters of the stabilizers.

• East Asian mathematical journal
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• v.7 no.1
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• pp.53-59
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• 1991