74,205 research outputs found
On vanishing sums of th roots of unity in finite fields
In an earlier work, the authors have determined all possible weights for
which there exists a vanishing sum of th roots
of unity in characteristic 0. In this paper, the same problem is
studied in finite fields of characteristic . For given and , results
are obtained on integers such that all integers are in the
``weight set'' . The main result in this paper guarantees,
under suitable conditions, the existence of solutions of
with all coordinates not equal to zero over a finite field
Face algebras and unitarity of SU(N)_L-TQFT
Using face algebras (i.e. algebras of L-operators of IRF models), we
construct modular tensor categories with positive definite inner product, whose
fusion rules and S-matrices are the same as (or slightly different from) those
obtained by at roots of unity. Also we obtain state-sums
of ABF models on framed links which give quantum SU(2)-invariants of
corresponding 3-manifolds.Comment: AMS-LaTeX, 36 pages, to appear in Commun. Math. Phy
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