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In this paper, we develop the Gr6bner-Shirshov basis theory for the representations of associative algebras by introducing the notion of Gr6bner-Shirshov pairs. Our result can be applied to solve the reduction problem in representation theory and to construct monomial bases of representations of associative algebras. As an illustration, we give an explicit… (More)

In [10], inspired by an idea of Gröbner, Buchberger discovered an effective algorithm for solving the reduction problem for commutative algebras, which is now called the Gröbner Basis Theory. It was generalized to associative algebras through Bergman’s Diamond Lemma [2], and the parallel theory for Lie algebras was developed by Shirshov [21]. The key… (More)

- Seok-Jin Kang, Dong-il Lee, Kyu-Hwan Lee, Hyungju Park, Efim Zelmanov
- 2007

We construct a new efficient algorithm for finding Gröbner–Shirshov bases for noncommutative algebras and their representations. This algorithm uses the Macaulay matrix [F.S. Macaulay, On some formula in elimination, Proc. London Math. Soc. 33 (1) (1902) 3–27], and can be viewed as a representation theoretic analogue of the F4 algorithm developed by J.C.… (More)

- Henry H. Kim, Kyu-Hwan Lee
- 2011

In this paper, we interpret the Gindikin–Karpelevich formula and the Casselman–Shalika formula as sums over Kashiwara–Lusztig’s canonical bases, generalizing the results of Bump and Nakasuji (2010) [7] to arbitrary split reductive groups. We also rewrite formulas for spherical vectors and zonal spherical functions in terms of canonical bases. In a… (More)

- Henry H. Kim, Kyu-Hwan Lee
- 2014

Article history: Received 20 August 2013 Available online xxxx Communicated by Dihua Jiang MSC: primary 17B67 secondary 11F22, 11F41

We show that a set of monic polynomials in the free Lie superalgebra is a Gröbner-Shirshov basis for a Lie superalgebra if and only if it is a Gröbner-Shirshov basis for its universal enveloping algebra. We investigate the structure of GröbnerShirshov bases for Kac-Moody superalgebras and give explicit constructions of Gröbner-Shirshov bases for classical… (More)

- Byungjin Cho, Jongwon Yoon, +9 authors Myung Gwan Hahm
- ACS applied materials & interfaces
- 2015

We report the production of a two-dimensional (2D) heterostructured gas sensor. The gas-sensing characteristics of exfoliated molybdenum disulfide (MoS2) connected to interdigitated metal electrodes were investigated. The MoS2 flake-based sensor detected a NO2 concentration as low as 1.2 ppm and exhibited excellent gas-sensing stability. Instead of metal… (More)

- Kyu-Hwan Lee, Henry H. Kim
- 2013

In this paper we consider the hyperbolic Kac–Moody algebra F associated with the generalized Cartan matrix ( 2 −2 0 −2 2 −1 0 −1 2 ) . Its connection to Siegel modular forms of genus 2 was first studied by A. Feingold and I. Frenkel. The denominator function of F is not an automorphic form. However, Gritsenko and Nikulin extended F to a generalized… (More)

- Kyu-Hwan Lee, Ben Salisbury
- J. Comb. Theory, Ser. A
- 2012

- Gabriel Feinberg, Kyu-Hwan Lee
- 2015

In this paper, we decompose the set of fully commutative elements into natural subsets when the Coxeter group is of type Dn, and study combinatorics of these subsets, revealing hidden structures. (We do not consider type An first, since a similar decomposition for type An is trivial.) As an application, we classify and enumerate the homogeneous… (More)