In-Sok Lee

Hecke algebras, Specht modules and Grobner-Shirshov bases

Abstract In this paper, we study the structure of Specht modules over Hecke algebras using the Grobner–Shirshov basis theory for the representations of associative algebras. The Grobner–Shirshov basis theory enables us to construct Specht modules in terms of generators and relations. Given a Specht module Sqλ, we determine the Grobner–Shirshov pair ( R q , R q λ ) and the monomial basis G(λ) consisting of standard monomials. We show that the monomials in G(λ) can be parameterized by the cozy tableaux. Using the division algorithm together with the monomial basis G(λ), we obtain a recursive algorithm of computing the Gram matrices. We discuss its applications to several interesting examples including Temperley–Lieb algebras.

Variants of the distinguished point method for cryptanalytic time memory trade-offs

The time memory trade-off (TMTO) algorithm, first introduced by Hellman, is a method for quickly inverting a one-way function, using pre-computed tables. The distinguished point method (DP) is a technique that reduces the number of table lookups performed by Hellmans algorithm. In this paper we propose a new variant of the DP technique, named variable DP (VDP), having properties very different from DP. It has an effect on the amount of memory required to store the pre-computed tables. We also show how to combine variable chain length techniques like DP and VDP with a more recent trade-off algorithm called the rainbow table method.

Representations of Ariki–Koike Algebras and Gröbner–Shirshov Bases

In this paper, we investigate the structure of Ariki?Koike algebras and their Specht modules using Grobner?Shirshov basis theory and combinatorics of Young tableaux. For a multipartition

On the Security of MOR Public Key Cryptosystem

\lambda

Analysis on a generalized algorithm for the strong discrete logarithm problem with auxiliary inputs

, we find a presentation of the Specht module

CELLULAR ALGEBRAS AND CENTERS OF HECKE ALGEBRAS

S^{\lambda}

Cyclotomic units in z p -extensions

given by generators and relations, and determine its Grobner?Shirshov pair. As a consequence, we obtain a linear basis of

Lie Algebras and Their Representations

S^{\lambda}

Gauss sums for O (2n,q)

consisting of standard monomials with respect to the Grobner?Shirshov pair. We show that this monomial basis can be canonically identified with the set of cozy tableaux of shape

Representations of ArikiKoike algebras and GrbnerShirshov bases

\lambda