327,926 research outputs found
Hecke Modules from Metaplectic Ice
We present a new framework for a broad class of affine Hecke algebra modules,
and show that such modules arise in a number of settings involving
representations of -adic groups and -matrices for quantum groups.
Instances of such modules arise from (possibly non-unique) functionals on
-adic groups and their metaplectic covers, such as the Whittaker
functionals. As a byproduct, we obtain new, algebraic proofs of a number of
results concerning metaplectic Whittaker functions. These are thus expressed in
terms of metaplectic versions of Demazure operators, which are built out of
-matrices of quantum groups depending on the cover degree and associated
root system
Global L^r-estimates and regularizing effect for solutions to the p(t, x) -Laplacian systems
We consider the initial boundary value problem for the p(t, x)-Laplacian
system in a bounded domain \Omega. If the initial data belongs to L^{r_0}, r_0
\geq 2, we give a global L^{r_0}({\Omega})-regularity result uniformly in t>0
that, in the particular case r_0 =\infty, implies a maximum modulus theorem.
Under the assumption p- = \inf p(t, x) > 2n/(n+r_0), we also state L^{r_0}- L^r
estimates for the solution, for r \geq r_0. Complete proofs of the results
presented here are given in the paper [F. Crispo, P. Maremonti, M. Ruzicka,
Global L^r-estimates and regularizing effect for solutions to the p(t, x)
-Laplacian systems, accepted for publication on Advances in Differential
Equations, 2017]
On lengths of proofs in non-classical logics
AbstractWe give proofs of the effective monotone interpolation property for the system of modal logic K, and others, and the system IL of intuitionistic propositional logic. Hence we obtain exponential lower bounds on the number of proof-lines in those systems. The main results have been given in [P. Hrubeš, Lower bounds for modal logics, Journal of Symbolic Logic 72 (3) (2007) 941–958; P. Hrubeš, A lower bound for intuitionistic logic, Annals of Pure and Applied Logic 146 (2007) 72–90]; here, we give considerably simplified proofs, as well as some generalisations
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