4,402 research outputs found
Root data with group actions
Suppose is a field, is a connected reductive algebraic -group,
is a maximal -torus in , and is a finite group that acts on
. From the above, one obtains a root datum on which
acts. Provided that preserves a positive
system in , not necessarily invariant under , we construct
an inverse to this process. That is, given a root datum on which
acts appropriately, we show how to construct a pair
, on which acts as above.
Although the pair and the action of are canonical only up to
an equivalence relation, we construct a particular pair for which is
-quasisplit and fixes a -stable pinning of .
Using these choices, we can define a notion of taking "-fixed points"
at the level of equivalence classes, and this process is compatible with a
general "restriction" process for root data with -action.Comment: v2: one word inserted, one citation inserted, one reference updated,
one misspelling correcte
Formulae relating the Bernstein and Iwahori-Matsumoto presentations of an affine Hecke algebra
We give explicit formulae for certain elements occurring in the Bernstein
presentation of an affine Hecke algebra, in terms of the usual Iwahori-
Matsumoto generators. We utilize certain minimal expressions for said elements
and we give a sheaf-theoretic interpretation for the existence of these minimal
expressions.Comment: To appear, J. of Algebr
Review of the Overseas E-voting (OSEV) system used in the Australian Capital Territory
The Australian Capital Territory (ACT) contains the Australian
national capital Canberra; the territory has a 25-member legislative
assembly combing both state and local government functions. The
members of the assembly are elected using two electronic voting systems.
The first, the EVACS system, uses Direct-Recording Electronic
voting machines (DREs) to record the vast majority of ballots in physical
polling-places. Overseas voters can use the Overseas E-voting system
(OSEV) to vote online. In this paper we report on our review of the
OSEV system and we also reflect on the transparency of the process by
which the system was introduced
Affine Deligne-Lusztig varieties in affine flag varieties
This paper studies affine Deligne-Lusztig varieties in the affine flag
manifold of a split group. Among other things, it proves emptiness for certain
of these varieties, relates some of them to those for Levi subgroups, extends
previous conjectures concerning their dimensions, and generalizes the superset
method.Comment: 44 pages, 4 figures. Minor changes to font, references, and
acknowledgments. Improved introduction, other improvements in exposition, and
two new figures added, for a total of
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