3,566 research outputs found
Reducible means and reducible inequalities
It is well-known that if a real valued function acting on a convex set
satisfies the -variable Jensen inequality, for some natural number , then, for all , it fulfills the -variable Jensen
inequality as well. In other words, the arithmetic mean and the Jensen
inequality (as a convexity property) are both reducible. Motivated by this
phenomenon, we investigate this property concerning more general means and
convexity notions. We introduce a wide class of means which generalize the
well-known means for arbitrary linear spaces and enjoy a so-called reducibility
property. Finally, we give a sufficient condition for the reducibility of the
-convexity property of functions and also for H\"older--Minkowski type
inequalities
A multiplicative analogue of complex symplectic implosion
We introduce a multiplicative version of complex-symplectic implosion in the
case of SL(n, \C).
The universal multiplicative implosion for SL(n, \C) is an affine variety
and can be viewed as a nonreductive geometric invariant theory quotient. It
carries a torus action. and reductions by this action give the Steinberg fibres
of SL(n, \C). We also explain how the real symplectic group-valued universal
implosion introduced by Hurtubise, Jeffrey and Sjamaar may be identified inside
this space.Comment: To appear in European Journal of Mathematic
Partial maps with domain and range: extending Schein's representation
The semigroup of all partial maps on a set under the operation of composition admits a number of operations relating to the domain and range of a partial map. Of particular interest are the operations R and L returning the identity on the domain of a map and on the range of a map respectively. Schein [25] gave an axiomatic characterisation of the semigroups with R and L representable as systems of partial maps; the class is a finitely axiomatisable quasivariety closely related to ample semigroups (which were introduced—as type A semigroups—by Fountain, [7]). We provide an account of Schein's result (which until now appears only in Russian) and extend Schein's method to include the binary operations of intersection, of greatest common range restriction, and some unary operations relating to the set of fixed points of a partial map. Unlike the case of semigroups with R and L, a number of the possibilities can be equationally axiomatised
Matching of orbital integrals (transfer) and Roche Hecke algebra isomorphisms
Let be a non-Archimedan local field, a connected reductive group
defined and split over , and a maximal -split torus in . Let
be a depth zero character of the maximal compact subgroup
of . It gives by inflation a character of an Iwahori
subgroup of containing . From Roche,
defines a split endoscopic group of , and there is an injective
morphism of -algebras where is the
Hecke algebra of compactly supported -spherical functions on
and is an Iwahori subgroup of . This morphism restricts
to an injective morphism between the centers of the Hecke algebras.
We prove here that a certain linear combination of morphisms analogous to
realizes the transfer (matching of strongly -regular semisimple
orbital integrals). If , our result is unconditional only if
is large enough.Comment: 82 page
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