5,575 research outputs found
On depth zero L-packets for classical groups
By computing reducibility points of parabolically induced representations, we construct, to within at most two unramified quadratic characters, the Langlands parameter of an arbitrary depth zero irreducible cuspidal representation (Formula presented.) of a classical group (which may be not-quasi-split) over a non-archimedean local field of odd residual characteristic. From this, we can explicitly describe all the irreducible cuspidal representations in the union of one, two, or four (Formula presented.) -packets, containing (Formula presented.). These results generalize the work of DeBackerâReeder (in the case of classical groups) from regular to arbitrary tame Langlands parameters
On the transfer reducibility of certain Farrell-Hsiang groups
We show how the existing proof of the Farrell-Jones Conjecture for virtually
poly--groups can be improved to rely only on the usual inheritance
properties in combination with transfer reducibility as a sufficient criterion
for the validity of the conjecture.Comment: 18 page
Notes on conformal invariance of gauge fields
In Lagrangian gauge systems, the vector space of global reducibility
parameters forms a module under the Lie algebra of symmetries of the action.
Since the classification of global reducibility parameters is generically
easier than the classification of symmetries of the action, this fact can be
used to constrain the latter when knowing the former. We apply this strategy
and its generalization for the non-Lagrangian setting to the problem of
conformal symmetry of various free higher spin gauge fields. This scheme allows
one to show that, in terms of potentials, massless higher spin gauge fields in
Minkowski space and partially-massless fields in (A)dS space are not conformal
for spin strictly greater than one, while in terms of curvatures, maximal-depth
partially-massless fields in four dimensions are also not conformal, unlike the
closely related, but less constrained, maximal-depth Fradkin--Tseytlin fields.Comment: 38 page
Making Queries Tractable on Big Data with Preprocessing
A query class is traditionally considered tractable if there exists a polynomial-time (PTIME) algorithm to answer its queries. When it comes to big data, however, PTIME al-gorithms often become infeasible in practice. A traditional and effective approach to coping with this is to preprocess data off-line, so that queries in the class can be subsequently evaluated on the data efficiently. This paper aims to pro-vide a formal foundation for this approach in terms of com-putational complexity. (1) We propose a set of Î -tractable queries, denoted by Î T0Q, to characterize classes of queries that can be answered in parallel poly-logarithmic time (NC) after PTIME preprocessing. (2) We show that several natu-ral query classes are Î -tractable and are feasible on big data. (3) We also study a set Î TQ of query classes that can be ef-fectively converted to Î -tractable queries by re-factorizing its data and queries for preprocessing. We introduce a form of NC reductions to characterize such conversions. (4) We show that a natural query class is complete for Î TQ. (5) We also show that Î T0Q â P unless P = NC, i.e., the set Î T0Q of all Î -tractable queries is properly contained in the set P of all PTIME queries. Nonetheless, Î TQ = P, i.e., all PTIME query classes can be made Î -tractable via proper re-factorizations. This work is a step towards understanding the tractability of queries in the context of big data. 1
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