• Publications
  • Influence
Spiders for rank 2 Lie algebras
A spider is an axiomatization of the representation theory of a group, quantum group, Lie algebra, or other group or group-like object. It is also known as a spherical category, or a strict, monoidalExpand
Another proof of the alternating sign matrix conjecture
Author(s): Kuperberg, Greg | Abstract: Robbins conjectured, and Zeilberger recently proved, that there are 1!4!7!...(3n-2)!/n!/(n+1)!/.../(2n-1)! alternating sign matrices of order n. We give a newExpand
Alternating sign matrices and domino tilings
We introduce a family of planar regions, called Aztec diamonds, and study the ways in which these regions can be tiled by dominoes. Our main result is a generating function that not only gives theExpand
A Subexponential-Time Quantum Algorithm for the Dihedral Hidden Subgroup Problem
  • G. Kuperberg
  • Mathematics, Physics
  • SIAM J. Comput.
  • 14 February 2003
A quantum algorithm for the dihedral hidden subgroup problem (DHSP) with time and query complexity $2^{O(\sqrt{\log\ N})}$. Expand
Symmetry classes of alternating-sign matrices under one roof
In a previous article [math.CO/9712207], we derived the alternating-sign matrix (ASM) theorem from the Izergin-Korepin determinant for a partition function for square ice with domain wall boundary.Expand
What is a virtual link
Several authors have recently studied virtual knots and links because they admit invariants arising from R-matrices. We prove that every virtual link is uniquely represented by a link L SI in aExpand
We establish a 3-manifold invariant for each finite-dimensional, involutory Hopf algebra. If the Hopf algebra is a group algebra G, the invariant counts homomorphisms from the fundamental group ofExpand
Web bases for sl(3) are not dual canonical
We compare two natural bases for the invariant space of a tensor product of irreducible representations of A_2, or sl(3). One basis is the web basis, defined from a skein theory called theExpand
We derive an inductive, combinatorial definition of a polynomial-valued regular isotopy invariant of links and tangled graphs. We show that the invariant equals the Reshetikhin-Turaev invariantExpand
Alternating-Sign Matrices and Domino Tilings (Part I)
We introduce a family of planar regions, called Aztec diamonds, and study tilings of these regions by dominoes. Our main result is that the Aztec diamond of order n has exactly 2n(n+1)/2 dominoExpand