1,464 research outputs found
On subfactors arising from asymptotic representations of symmetric groups
We consider the infinite symmetric group and its infinite index subgroup
given as the stabilizer subgroup of one element under the natural action on a
countable set. This inclusion of discrete groups induces a hyperfinite
subfactor for each finite factorial representation of the larger group. We
compute subfactor invariants of this construction in terms of the Thoma
parameter.Comment: to appear in Proc. AM
A few remarks on the tube algebra of a monoidal category
We prove two results on the tube algebras of rigid C-tensor categories.
The first is that the tube algebra of the representation category of a compact
quantum group is a full corner of the Drinfeld double of . As an
application we obtain some information on the structure of the tube algebras of
the Temperley-Lieb categories for . The second result is that the
tube algebras of weakly Morita equivalent C-tensor categories are strongly
Morita equivalent. The corresponding linking algebra is described as the tube
algebra of the -category defining the Morita context.Comment: 17 pages; v4: minor changes and change of section numbering to the
published version, to appear in Proc. Edinb. Math. Soc.; v3: description of
the topology on the primitive spectrum of the tube algebra of a
Temperley-Lieb category (d>2), a few remarks and minor fixes; v2: rewritten
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