559 research outputs found
On the direct indecomposability of infinite irreducible Coxeter groups and the Isomorphism Problem of Coxeter groups
In this paper we prove, without the finite rank assumption, that any
irreducible Coxeter group of infinite order is directly indecomposable as an
abstract group. The key ingredient of the proof is that we can determine, for
an irreducible Coxeter group, the centralizers of the normal subgroups that are
generated by involutions. As a consequence, we show that the problem of
deciding whether two general Coxeter groups are isomorphic, as abstract groups,
is reduced to the case of irreducible Coxeter groups, without assuming the
finiteness of the number of the irreducible components or their ranks. We also
give a description of the automorphism group of a general Coxeter group in
terms of those of its irreducible components.Comment: 30 page
A coproduct structure on the formal affine Demazure algebra
In the present paper we generalize the coproduct structure on nil Hecke rings
introduced and studied by Kostant-Kumar to the context of an arbitrary
algebraic oriented cohomology theory and its associated formal group law. We
then construct an algebraic model of the T-equivariant oriented cohomology of
the variety of complete flags.Comment: 28 pages; minor revision of the previous versio
The nil Hecke ring and singularity of Schubert varieties
We give a criterion for smoothness of a point in any Schubert variety in any
G/B in terms of the nil Hecke ring.Comment: AMSTE
Coloured peak algebras and Hopf algebras
For a finite abelian group, we study the properties of general
equivalence relations on G_n=G^n\rtimes \SG_n, the wreath product of with
the symmetric group \SG_n, also known as the -coloured symmetric group. We
show that under certain conditions, some equivalence relations give rise to
subalgebras of \k G_n as well as graded connected Hopf subalgebras of
\bigoplus_{n\ge o} \k G_n. In particular we construct a -coloured peak
subalgebra of the Mantaci-Reutenauer algebra (or -coloured descent algebra).
We show that the direct sum of the -coloured peak algebras is a Hopf
algebra. We also have similar results for a -colouring of the Loday-Ronco
Hopf algebras of planar binary trees. For many of the equivalence relations
under study, we obtain a functor from the category of finite abelian groups to
the category of graded connected Hopf algebras. We end our investigation by
describing a Hopf endomorphism of the -coloured descent Hopf algebra whose
image is the -coloured peak Hopf algebra. We outline a theory of
combinatorial -coloured Hopf algebra for which the -coloured
quasi-symmetric Hopf algebra and the graded dual to the -coloured peak Hopf
algebra are central objects.Comment: 26 pages latex2
On the structure of Borel stable abelian subalgebras in infinitesimal symmetric spaces
Let g=g_0+g_1 be a Z_2-graded Lie algebra. We study the posets of abelian
subalgebras of g_1 which are stable w.r.t. a Borel subalgebra of g_0. In
particular, we find out a natural parametrization of maximal elements and
dimension formulas for them. We recover as special cases several results of
Kostant, Panyushev, Suter.Comment: Latex file, 35 pages, minor corrections, some examples added. To
appear in Selecta Mathematic
GALEX J201337.6+092801: The lowest gravity subdwarf B pulsator
We present the recent discovery of a new subdwarf B variable (sdBV), with an
exceptionally low surface gravity. Our spectroscopy of J20136+0928 places it at
Teff = 32100 +/- 500, log(g) = 5.15 +/- 0.10, and log(He/H) = -2.8 +/- 0.1.
With a magnitude of B = 12.0, it is the second brightest V361 Hya star ever
found. Photometry from three different observatories reveals a temporal
spectrum with eleven clearly detected periods in the range 376 to 566 s, and at
least five more close to our detection limit. These periods are unusually long
for the V361 Hya class of short-period sdBV pulsators, but not unreasonable for
p- and g-modes close to the radial fundamental, given its low surface gravity.
Of the ~50 short period sdB pulsators known to date, only a single one has been
found to have comparable spectroscopic parameters to J20136+0928. This is the
enigmatic high-amplitude pulsator V338 Ser, and we conclude that J20136+0928 is
the second example of this rare subclass of sdB pulsators located well above
the canonical extreme horizontal branch in the HR diagram.Comment: 5 pages, accepted for publication in ApJ Letter
Modifications in biphasic liquid-scintillation vial system for radiometry
Several modifications of the biphasic liquid-scintillation vial system for radiometry have been tried in order to improve the counting efficiency. The biphasic system consisted of an inner sterile vial containing medium and substrate, and an outer liquid-scintillation vial lined on the inside with filter paper impregnated with scintillation fluors and alkali. The system gave an overall counting efficiency of 14.6%. Substitution of methanolic NaOH for impregnation of the paper raised the counting efficiency to 29.1%. This could be further enhanced to 33.8% by lining only half of the outer vial with filter paper, thereby allowing improved optical transmission of scintillation light. Increasing the amount of fluor did not change the efficiency significantly. A complete interchange in the system, whereby half of the inner vial was lined with filter paper and was otherwise empty, while the outer vial contained the medium and substrate, gave the highest efficiency (36.9%). This also allowed the use of larger amounts of medium and the inoculum
Mask formulas for cograssmannian Kazhdan-Lusztig polynomials
We give two contructions of sets of masks on cograssmannian permutations that
can be used in Deodhar's formula for Kazhdan-Lusztig basis elements of the
Iwahori-Hecke algebra. The constructions are respectively based on a formula of
Lascoux-Schutzenberger and its geometric interpretation by Zelevinsky. The
first construction relies on a basis of the Hecke algebra constructed from
principal lower order ideals in Bruhat order and a translation of this basis
into sets of masks. The second construction relies on an interpretation of
masks as cells of the Bott-Samelson resolution. These constructions give
distinct answers to a question of Deodhar.Comment: 43 page
The Kazhdan-Lusztig conjecture for finite W-algebras
We study the representation theory of finite W-algebras. After introducing
parabolic subalgebras to describe the structure of W-algebras, we define the
Verma modules and give a conjecture for the Kac determinant. This allows us to
find the completely degenerate representations of the finite W-algebras. To
extract the irreducible representations we analyse the structure of singular
and subsingular vectors, and find that for W-algebras, in general the maximal
submodule of a Verma module is not generated by singular vectors only.
Surprisingly, the role of the (sub)singular vectors can be encapsulated in
terms of a `dual' analogue of the Kazhdan-Lusztig theorem for simple Lie
algebras. These involve dual relative Kazhdan-Lusztig polynomials. We support
our conjectures with some examples, and briefly discuss applications and the
generalisation to infinite W-algebras.Comment: 11 page
Quantum Pieri rules for isotropic Grassmannians
We study the three point genus zero Gromov-Witten invariants on the
Grassmannians which parametrize non-maximal isotropic subspaces in a vector
space equipped with a nondegenerate symmetric or skew-symmetric form. We
establish Pieri rules for the classical cohomology and the small quantum
cohomology ring of these varieties, which give a combinatorial formula for the
product of any Schubert class with certain special Schubert classes. We also
give presentations of these rings, with integer coefficients, in terms of
special Schubert class generators and relations.Comment: 59 pages, LaTeX, 6 figure
- …