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630
Longest increasing subsequences: from patience sorting to the BaikDeiftJohansson theorem
 BULL. AMER. MATH. SOC. (N.S
, 1999
"... We describe a simple oneperson card game, patience sorting. Its analysis leads to a broad circle of ideas linking Young tableaux with the longest increasing subsequence of a random permutation via the Schensted correspondence. A recent highlight of this area is the work of BaikDeiftJohansson wh ..."
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Cited by 183 (2 self)
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We describe a simple oneperson card game, patience sorting. Its analysis leads to a broad circle of ideas linking Young tableaux with the longest increasing subsequence of a random permutation via the Schensted correspondence. A recent highlight of this area is the work of BaikDeiftJohansson which yields limiting probability laws via hard analysis of Toeplitz determinants.
Hecke algebras at roots of unity and crystal bases of quantum affine algebras
, 1995
"... We present a fast algorithm for computing the global crystal basis of the basic Uq(bsln)module. This algorithm is based on combinatorial techniques which have been developed for dealing with modular representations of symmetric groups, and more generally with representations of Hecke algebras of ty ..."
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Cited by 164 (17 self)
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We present a fast algorithm for computing the global crystal basis of the basic Uq(bsln)module. This algorithm is based on combinatorial techniques which have been developed for dealing with modular representations of symmetric groups, and more generally with representations of Hecke algebras of type A at roots of unity. We conjecture that, upon specialization q! 1, our algorithm computes the decomposition matrices of all Hecke algebras at a nth root of 1.
The (Q, q)Schur Algebra
 PROC. LONDON MATH. SOC
, 1999
"... In this paper we use the Hecke algebra of type B to define a new algebra S which is an analogue of the qSchur algebra. We construct Weyl modules for S and obtain, as factor modules, a family of irreducible S{modules over any field. ..."
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Cited by 112 (13 self)
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In this paper we use the Hecke algebra of type B to define a new algebra S which is an analogue of the qSchur algebra. We construct Weyl modules for S and obtain, as factor modules, a family of irreducible S{modules over any field.
Advanced determinant calculus: a complement
 LINEAR ALGEBRA APPL
, 2005
"... This is a complement to my previous article “Advanced Determinant Calculus ” (Séminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described in the previous article in order to solve a particular probl ..."
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Cited by 89 (8 self)
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This is a complement to my previous article “Advanced Determinant Calculus ” (Séminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described in the previous article in order to solve a particular problem from number theory (G. Almkvist, J. Petersson and the author, Experiment. Math. 12 (2003), 441– 456). Moreover, I add a list of determinant evaluations which I consider as interesting, which have been found since the appearance of the previous article, or which I failed to mention there, including several conjectures and open problems.
Branching rules for modular representations of symmetric groups III: Some . . .
 J. LONDON MATH. SOC
, 1996
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qSchur algebras and complex reflection groups
"... Abstract. We show that the category O for a rational Cherednik algebra of type A is equivalent to modules over a qSchur algebra (parameter ̸ ∈ 1 2 + Z), providing thus character formulas for simple modules. We give some generalization to Bn(d). We prove an “abstract ” translation principle. These r ..."
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Cited by 58 (2 self)
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Abstract. We show that the category O for a rational Cherednik algebra of type A is equivalent to modules over a qSchur algebra (parameter ̸ ∈ 1 2 + Z), providing thus character formulas for simple modules. We give some generalization to Bn(d). We prove an “abstract ” translation principle. These results follow from the unicity of certain highest weight categories covering Hecke algebras. We also provide a semisimplicity criterion for Hecke algebras of complex reflection groups. 1.
Generalized FFTs  A Survey Of Some Recent Results
, 1995
"... In this paper we survey some recent work directed towards generalizing the fast Fourier transform (FFT). We work primarily from the point of view of group representation theory. In this setting the classical FFT can be viewed as a family of efficient algorithms for computing the Fourier transform of ..."
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Cited by 57 (7 self)
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In this paper we survey some recent work directed towards generalizing the fast Fourier transform (FFT). We work primarily from the point of view of group representation theory. In this setting the classical FFT can be viewed as a family of efficient algorithms for computing the Fourier transform of either a function defined on a finite abelian group, or a bandlimited function on a compact abelian group. We discuss generalizations of the FFT to arbitrary finite groups and compact Lie groups.