344 research outputs found
Modular classes of Poisson-Nijenhuis Lie algebroids
The modular vector field of a Poisson-Nijenhuis Lie algebroid is defined
and we prove that, in case of non-degeneracy, this vector field defines a
hierarchy of bi-Hamiltonian -vector fields. This hierarchy covers an
integrable hierarchy on the base manifold, which may not have a
Poisson-Nijenhuis structure.Comment: To appear in Letters in Mathematical Physic
Weak splittings of quotients of Drinfeld and Heisenberg doubles
We investigate the fine structure of the simplectic foliations of Poisson
homogeneous spaces. Two general results are proved for weak splittings of
surjective Poisson submersions from Heisenberg and Drinfeld doubles. The
implications of these results are that the torus orbits of symplectic leaves of
the quotients can be explicitly realized as Poisson-Dirac submanifolds of the
torus orbits of the doubles. The results have a wide range of applications to
many families of real and complex Poisson structures on flag varieties. Their
torus orbits of leaves recover important families of varieties such as the open
Richardson varieties.Comment: 20 pages, AMS Late
Formal Hecke algebras and algebraic oriented cohomology theories
In the present paper we generalize the construction of the nil Hecke ring of
Kostant-Kumar to the context of an arbitrary algebraic oriented cohomology
theory of Levine-Morel and Panin-Smirnov, e.g. to Chow groups, Grothendieck's
K_0, connective K-theory, elliptic cohomology, and algebraic cobordism. The
resulting object, which we call a formal (affine) Demazure algebra, is
parameterized by a one-dimensional commutative formal group law and has the
following important property: specialization to the additive and multiplicative
periodic formal group laws yields completions of the nil Hecke and the 0-Hecke
rings respectively. We also introduce a deformed version of the formal (affine)
Demazure algebra, which we call a formal (affine) Hecke algebra. We show that
the specialization of the formal (affine) Hecke algebra to the additive and
multiplicative periodic formal group laws gives completions of the degenerate
(affine) Hecke algebra and the usual (affine) Hecke algebra respectively. We
show that all formal affine Demazure algebras (and all formal affine Hecke
algebras) become isomorphic over certain coefficient rings, proving an analogue
of a result of Lusztig.Comment: 28 pages. v2: Some results strengthened and references added. v3:
Minor corrections, section numbering changed to match published version. v4:
Sign errors in Proposition 6.8(d) corrected. This version incorporates an
erratum to the published versio
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The Next Big Match: Convergence, Competition and Sports Media Rights
Using examples from a number of different European countries, this article analyses the increasingly prominent position of traditional telecommunications companies, such as British Telecom (UK), Deutsche Telekom (Germany), France Telecom/Orange (France) and Telefonica (Spain), in the contemporary sports media rights market. The first part of the article examines the commercial strategies of telecommunications operators and highlights how their acquisition of sports rights has been driven by the need to ensure a competitive position within an increasingly converged communications market. The second part of the article then moves on to consider the regulation of the sports media rights market. Most significantly, this section emphasises the need for further regulatory intervention to ensure that increased competition for sports rights leads to improved services and lower prices for consumers, rather than merely endlessly spiralling fees for the exclusive ownership of premium rights that are then passed on to sports channel and/or broadband subscribers
Integral Grothendieck-Riemann-Roch theorem
We show that, in characteristic zero, the obvious integral version of the
Grothendieck-Riemann-Roch formula obtained by clearing the denominators of the
Todd and Chern characters is true (without having to divide the Chow groups by
their torsion subgroups). The proof introduces an alternative to Grothendieck's
strategy: we use resolution of singularities and the weak factorization theorem
for birational maps.Comment: 24 page
Support varieties for selfinjective algebras
Support varieties for any finite dimensional algebra over a field were
introduced by Snashall-Solberg using graded subalgebras of the Hochschild
cohomology. We mainly study these varieties for selfinjective algebras under
appropriate finite generation hypotheses. Then many of the standard results
from the theory of support varieties for finite groups generalize to this
situation. In particular, the complexity of the module equals the dimension of
its corresponding variety, all closed homogeneous varieties occur as the
variety of some module, the variety of an indecomposable module is connected,
periodic modules are lines and for symmetric algebras a generalization of
Webb's theorem is true
Finite Schur filtration dimension for modules over an algebra with Schur filtration
Let G be GL_N or SL_N as reductive linear algebraic group over a field k of
positive characteristic p. We prove several results that were previously
established only when N 2^N. Let G act rationally on a finitely
generated commutative k-algebra A. Assume that A as a G-module has a good
filtration or a Schur filtration. Let M be a noetherian A-module with
compatible G action. Then M has finite good/Schur filtration dimension, so that
there are at most finitely many nonzero H^i(G,M). Moreover these H^i(G,M) are
noetherian modules over the ring of invariants A^G. Our main tool is a
resolution involving Schur functors of the ideal of the diagonal in a product
of Grassmannians.Comment: 22 pages; final versio
Continuous non-perturbative regularization of QED
We regularize in a continuous manner the path integral of QED by construction
of a non-local version of its action by means of a regularized form of Dirac's
functions. Since the action and the measure are both invariant under
the gauge group, this regularization scheme is intrinsically non-perturbative.
Despite the fact that the non-local action converges formally to the local one
as the cutoff goes to infinity, the regularized theory keeps trace of the
non-locality through the appearance of a quadratic divergence in the transverse
part of the polarization operator. This term which is uniquely defined by the
choice of the cutoff functions can be removed by a redefinition of the
regularized action. We notice that as for chiral fermions on the lattice, there
is an obstruction to construct a continuous and non ambiguous regularization in
four dimensions. With the help of the regularized equations of motion, we
calculate the one particle irreducible functions which are known to be
divergent by naive power counting at the one loop order.Comment: 23 pages, LaTeX, 5 Encapsulated Postscript figures. Improved and
revised version, to appear in Phys. Rev.
Strategic Transformations in the Media
Digital technologies have transformed the way many media organisations have conducted their business over the past two decades. This transformational context raises a number of important questions for media management researchers. Firstly, how have media firms adapted their strategies, resources and capabilities in response to the challenges presented by an increasingly digital environment? Secondly, how have these adaptive practices affected their corporate financial performance? This paper advances our theoretical understanding of media firm transformation by using a multi-disciplinary approach that draws on knowledge from corporate strategy, dynamic capabilities and firm performance. This integrated approach provides a more holistic view of strategic business transformation by understanding the strategic arguments that compel firm’s to reconfigure their resources and capabilities in a dynamic business environment
Multiplicative slices, relativistic Toda and shifted quantum affine algebras
We introduce the shifted quantum affine algebras. They map homomorphically
into the quantized -theoretic Coulomb branches of SUSY
quiver gauge theories. In type , they are endowed with a coproduct, and they
act on the equivariant -theory of parabolic Laumon spaces. In type ,
they are closely related to the open relativistic quantum Toda lattice of type
.Comment: 125 pages. v2: references updated; in section 11 the third local Lax
matrix is introduced. v3: references updated. v4=v5: 131 pages, minor
corrections, table of contents added, Conjecture 10.25 is now replaced by
Theorem 10.25 (whose proof is based on the shuffle approach and is presented
in a new Appendix). v6: Final version as published, references updated,
footnote 4 adde
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