• Honam Mathematical Journal
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• v.35 no.1
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• pp.73-82
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• 2013

There are some identities between the representations of Hecke operators defined on a subspace of modular forms associated with orders of a Quaternion algebra. In this paper, we find the identities between the zeta functions attached to these representations.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1373-1388
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• 2020

In the paper, we give an explicit basis of the cyclotomic quiver Hecke algebra corresponding to a minuscule representation of finite type.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.71-79
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• 2002

In this short note, we find bases of the centers of generic Hecke algebras associated with certain finite Coxeter groups. Our bases are described using the notion of cell datum of Graham and Lehrer, and the notion of norm.

• 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.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.739-746
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• 2013

There are several ways to normalize a Haar measure on the orders in a quaternion algebra. In order to understand the arithmetic properties of orders, we study the volumes of orders and compute them for some cases.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.365-378
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• 2004

The orders in quaternion algebras play central role in the theory of Hecke operators. In this paper, we study the order of two sided ideal group in orders of a quaternion algebra.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.611-632
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• 2009

The orders in a quaternion algebra play a central role of the theory of Hecke operators. In this paper, we study the arithmetic properties of optimal embeddings of orders in a quaternion algebra over a dyadic local field.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.343-358
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• 2008

The primitive orders in a quaternion algebra play a central role of the theory of Hecke operators. In this paper, we study theta series generated by Brandt matrices and its applications to almost Ramanujan graphs.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.821-829
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• 2006

We determine reducibility points of degenerate principal series for exceptional p-adic groups of type $G_2$ via Jacquet module techniques and Hecke algebra isomorphisms.