3,475 research outputs found
Quantum supergroups and topological invariants of three - manifolds
The Reshetikhin - Turaeve approach to topological invariants of three -
manifolds is generalized to quantum supergroups. A general method for
constructing three - manifold invariants is developed, which requires only the
study of the eigenvalues of certain central elements of the quantum supergroup
in irreducible representations. To illustrate how the method works,
at odd roots of unity is studied in detail, and the
corresponding topological invariants are obtained.Comment: 22 page
P versus NP and geometry
I describe three geometric approaches to resolving variants of P v. NP,
present several results that illustrate the role of group actions in complexity
theory, and make a first step towards completely geometric definitions of
complexity classes.Comment: 20 pages, to appear in special issue of J. Symbolic. Comp. dedicated
to MEGA 200
All degree six local unitary invariants of k qudits
We give explicit index-free formulae for all the degree six (and also degree
four and two) algebraically independent local unitary invariant polynomials for
finite dimensional k-partite pure and mixed quantum states. We carry out this
by the use of graph-technical methods, which provides illustrations for this
abstract topic.Comment: 18 pages, 6 figures, extended version. Comments are welcom
Generalized Littlewood-Richardson coefficients for branching rules of GL(n) and extremal weight crystals
Following the methods used by Derksen-Weyman in \cite{DW11} and Chindris in
\cite{Chi08}, we use quiver theory to represent the generalized
Littlewood-Richardson coefficients for the branching rule for the diagonal
embedding of \gl(n) as the dimension of a weight space of semi-invariants.
Using this, we prove their saturation and investigate when they are nonzero. We
also show that for certain partitions the associated stretched polynomials
satisfy the same conjectures as single Littlewood-Richardson coefficients. We
then provide a polytopal description of this multiplicity and show that its
positivity may be computed in strongly polynomial time. Finally, we remark that
similar results hold for certain other generalized Littlewood-Richardson
coefficients.Comment: 28 pages, comments welcom
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