• 호남수학학술지
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• 제35권1호
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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.

• 대한수학회지
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• 제57권6호
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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.

• 대한수학회보
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• 제39권1호
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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.

• 대한수학회지
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• 제40권1호
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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.

• 호남수학학술지
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• 제35권4호
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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.

• 호남수학학술지
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• 제26권4호
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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.

• 호남수학학술지
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• 제31권4호
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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.

• 호남수학학술지
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• 제30권2호
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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.

• 대한수학회보
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• 제43권4호
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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.