420 research outputs found
Hecke algebras of finite type are cellular
Let \cH be the one-parameter Hecke algebra associated to a finite Weyl
group , defined over a ground ring in which ``bad'' primes for are
invertible. Using deep properties of the Kazhdan--Lusztig basis of \cH and
Lusztig's \ba-function, we show that \cH has a natural cellular structure
in the sense of Graham and Lehrer. Thus, we obtain a general theory of ``Specht
modules'' for Hecke algebras of finite type. Previously, a general cellular
structure was only known to exist in types and .Comment: 14 pages; added reference
Exact solutions of two complementary 1D quantum many-body systems on the half-line
We consider two particular 1D quantum many-body systems with local
interactions related to the root system . Both models describe identical
particles moving on the half-line with non-trivial boundary conditions at the
origin, and they are in many ways complementary to each other. We discuss the
Bethe Ansatz solution for the first model where the interaction potentials are
delta-functions, and we find that this provides an exact solution not only in
the boson case but even for the generalized model where the particles are
distinguishable. In the second model the particles have particular momentum
dependent interactions, and we find that it is non-trivial and exactly solvable
by Bethe Ansatz only in case the particles are fermions. This latter model has
a natural physical interpretation as the non-relativistic limit of the massive
Thirring model on the half-line. We establish a duality relation between the
bosonic delta-interaction model and the fermionic model with local momentum
dependent interactions. We also elaborate on the physical interpretation of
these models. In our discussion the Yang-Baxter relations and the Reflection
equation play a central role.Comment: 15 pages, a mistake corrected changing one of our conclusion
Schur elements for the Ariki-Koike algebra and applications
We study the Schur elements associated to the simple modules of the
Ariki-Koike algebra. We first give a cancellation-free formula for them so that
their factors can be easily read and programmed. We then study direct
applications of this result. We also complete the determination of the
canonical basic sets for cyclotomic Hecke algebras of type in
characteristic 0.Comment: The paper contains the results of arXiv:1101.146
Centers and Cocenters of -Hecke algebras
In this paper, we give explicit descriptions of the centers and cocenters of
-Hecke algebras associated to finite Coxeter groups.Comment: 13 pages, a mistake in 4.2 is correcte
Affine cellularity of affine Hecke algebras of rank two
We show that affine Hecke algebras of rank two with generic parameters are
affine cellular in the sense of Koenig-Xi.Comment: 24 pages, 4 figures and 14 tables. New version: added references,
corrected typos. Final versio
Hecke algebras with unequal parameters and Vogan's left cell invariants
In 1979, Vogan introduced a generalised -invariant for characterising
primitive ideals in enveloping algebras. Via a known dictionary this translates
to an invariant of left cells in the sense of Kazhdan and Lusztig. Although it
is not a complete invariant, it is extremely useful in describing left cells.
Here, we propose a general framework for defining such invariants which also
applies to Hecke algebras with unequal parameters.Comment: 15 pages. arXiv admin note: substantial text overlap with
arXiv:1405.573
On Kazhdan-Lusztig cells in type B
32 pagesWe prove that, for any choice of parameters, the Kazhdan-Lusztig cells of a Weyl group of type are unions of combinatorial cells (defined using the domino insertion algorithm)
Enumeration of bigrassmannian permutations below a permutation in Bruhat order
In theory of Coxeter groups, bigrassmannian elements are well known as
elements which have precisely one left descent and precisely one right descent.
In this article, we prove formulas on enumeration of bigrassmannian
permutations weakly below a permutation in Bruhat order in the symmetric
groups. For the proof, we use equivalent characterizations of bigrassmannian
permutations by Lascoux-Schutzenberger and Reading.Comment: 7 pages
Estrogen Regulation of Jun and Fos in MCF-7 Cells
Abstract C-Fos and c-Jun are transcription factors that form the dimer Activator Protein 1 (AP-1) and bind DNA to initiate transcription. C-Fos, c-Jun are targets of the Extracellular Signal-Regulated Kinase (ERK) in multiple cell types, including MCF-7 breast cancer cells. The hormone estrogen (E2) can increase intracellular calcium levels which activates calcium/calmodulin-dependent kinase (CaM Kinase) proteins, which control ERK and gene transcription. Our goal was to evaluate the ability of E2 to activate c-Fos and c-Jun and induce their dimerization, via CaM KK and ERK, in MCF-7 cells. Interestingly, E2 stimulation of MCF-7 cells triggered phosphorylation of c-Jun and c-Fos an effect that was blocked with STO-609 and U0126, which target CaM KK and ERK, respectively. siRNA inhibition of CaM KK and ERK blocked E2-stimulated c-Jun and c-Fos phosphorylation. Additionally, E2 triggered AP-1 directed luciferase activity in MCF-7 cells that was blocked by inhibiting either CaM KK or ERK with siRNA. In summary, our data suggests that E2 utilizes both CaM KK and ERK to phosphorylate c-Jun and c-Fos and regulate their transcriptional activity in breast cancer cells
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