scispace - formally typeset
Search or ask a question
JournalISSN: 0012-7094

Duke Mathematical Journal 

Duke University Press
About: Duke Mathematical Journal is an academic journal published by Duke University Press. The journal publishes majorly in the area(s): Conjecture & Bounded function. It has an ISSN identifier of 0012-7094. Over the lifetime, 5911 publications have been published receiving 255315 citations. The journal is also known as: DMJ.


Papers
More filters
Journal ArticleDOI
TL;DR: In this article, the existence and uniqueness of crystal bases for an arbitrary symmetrizable Kac-Moody Lie algebra I was proved for the case when g is one of the classical Lie algebras A, B, C, and D,. K.
Abstract: 0. Introduction. The notion of the q-analogue of universal enveloping algebras is introduced independently by V. G. Drinfeld and M. Jimbo in 1985 in their study of exactly solvable models in the statistical mechanics. This algebra Uq(g) contains a parameter q, and, when q 1, this coincides with the universal enveloping algebra. In the context of exactly solvable models, the parameter q is that of temperature, and q 0 corresponds to the absolute temperature zero. For that reason, we can expect that the q-analogue has a simple structure at q 0. In [K1] we named crystallization the study at q 0, and we introduced the notion of crystal bases. Roughly speaking, crystal bases are bases of Uq(9)-modules at q 0 that satisfy certain axioms. There, we proved the existence and the uniqueness of crystal bases of finite-dimensional representations of U(g) when g is one of the classical Lie algebras A,, B,, C, and D,. K. Misra and T. Miwa ([M]) proved the existence of a crystal base of the basic representation of U,(A1)) and gave its combinatorial description. The aim of this article is to give the proof of the existence and uniqueness theorem of crystal bases for an arbitrary symmetrizable Kac-Moody Lie algebra I. Moreover, we globalize this notion. Namely, with the aid of a crystal base we construct a base named the global crystal base of any highest weight irreducible integrable

1,420 citations

Journal ArticleDOI
TL;DR: In this paper, the authors give a complete solution when S is a quadratic surface given by the duality argument for the special case S {(x, y) yZ xz I} and give the interpretation of the answer as a space-time decay for solutions of the Klein-Gordon equation with finite relativistic invariant norm.
Abstract: A simple duality argument shows these two problems are completely equivalent ifp and q are dual indices, (]/) + (I/q) ]. ]nteresl in Problem A when S is a sphere stems from the work of C. Fefferman [3], and in this case the answer is known (see [l I]). Interest in Problem B was recently signalled by 1. Segal [6] who studied the special case S {(x, y) yZ xz I} and gave the interpretation of the answer as a space-time decay for solutions of the Klein-Gordon equation with finite relativistic-invariant norm. In this paper we give a complete solution when S is a quadratic surface given by

1,351 citations

Journal ArticleDOI
TL;DR: In this article, Khovanov et al. constructed a bigraded cohomology theory of links whose Euler characteristic is the Jones polynomial, and proved that it is the case for all links.
Abstract: Author(s): Khovanov, Mikhail | Abstract: We construct a bigraded cohomology theory of links whose Euler characteristic is the Jones polynomial.

1,123 citations

Performance
Metrics
No. of papers from the Journal in previous years
YearPapers
202338
202267
202174
202066
201965
201863