1,721,353 research outputs found
Closures of orbits under the diagonal action in the wonderful compactification of PGL(3)
No full textWe study the orbits under the diagonal action of a semisimple adjoint
group G on its wonderful compactification X for the case G = PGL(3) and determine
the closure relations between such orbits. Moreover we show an example in the wonderful
compactification of PSp(4) in which the closure of an orbit for the diagonal action consists
of infinitely many orbits
A homological interpretation of the transverse quiver grassmannians
No full textIn recent articles, the investigation of atomic bases in cluster algebras
associated to affine quivers led the second–named author to introduce a variety
called transverse quiver Grassmannian and the first–named and third–named authors
to consider the smooth loci of quiver Grassmannians. In this paper, we prove that,
for any affine quiver Q, the transverse quiver Grassmannian of an indecomposable
representation M is the set of points N in the quiver Grassmannian of M such that
Ext1(N,M/N) = 0.As a corollary we prove that the transverse quiver Grassmannian
coincides with the smooth locus of the irreducible components of minimal dimension
in the quiver Grassmannian
A note on fontaine theory using different Lubin-Tate groups
No full textThe starting point of Fontaine theory is the possibility of translating the study of a p-adic representation of the absolute Galois group of a finite extension K of Qp into the investigation of a (φ, Γ)-module. This is done by decomposing the Galois group along a totally ramified extension of K, via the theory of the field of norms: the extension used is obtained by means of the cyclotomic tower which, in turn, is associated to the multiplicative Lubin-Tate group. It is known that one can insert different Lubin-Tate groups into the "Fontaine theory" machine to obtain equivalences with new categories of (φ, Γ)-modules (here φ may be iterated). This article uses only (φ, Γ)-theoretical terms to compare the different (φ, Γ) modules arising from various Lubin-Tate groups
On a theorem of Schmid
No full textWe establish for which parabolic subgroups P of a simply connected and semisimple algebraic group G with unipotent radical U and Levi factor H the two rings k[G/H]U and k[U^−] are isomorphic as H algebras. We show the relation of this problem with a Theorem of Schmid and we compare the multiplications in the rings k[U^−] and k[G/H]
On sheets of conjugacy classes in good characteristic
No full textWe show that the sheets for a connected reductive algebraic group over an algebraically closed field in good characteristic acting on itself by
conjugation are in bijection with -orbits of triples where is the connected centralizer of a semisimple element in ,
is a suitable coset in and is a rigid unipotent conjugacy class in ; or, equivalently they are
in bijection with -orbits of pairs with a Levi factor of a parabolic subgroup of and a rigid conjugacy class of .
Any semisimple element is contained in a unique sheet and corresponds to a triple with .
The sheets in containing a unipotent conjugacy class are precisely those corresponding to triples for which is a Levi factor of a parabolic subgroup of and the
class is unique
A Katsylo theorem for sheets of spherical conjugacy classes
Full text linkWe show that, for a sheet or a Lusztig stratum S containing spherical conjugacy classes in a connected reductive algebraic group G over an algebraically closed field in good characteristic, the orbit space S/G is isomorphic to the quotient of an affine subvariety of G modulo the action of a finite abelian 2-group. The affine subvariety is a closed subset of a Bruhat double coset and the abelian group is a finite subgroup of a maximal torus of G. We show that sheets of spherical conjugacy classes in a simple group are always smooth and we list which strata containing spherical classes are smooth
GEOMETRY OF QUIVER GRASSMANNIANS OF KRONECKER TYPE AND APPLICATIONS TO CLUSTER ALGEBRAS
Full text linkWe study quiver Grassmannians associated with indecomposable representations (of finite dimension) of the Kronecker quiver. We find a cellular decomposition for them and we compute their Betti numbers. As an application, we find a geometric realization for the atomic basis of cluster algebras of type A(1)((1)) found by Sherman and Zelevinsky (who called it the canonical basis) and those of type A(2)((1)) found in an earlier paper of the first author
A correlation study between aerosol size distribution and meteorological parameters for a desertic area in Namibia.
No full textA seasonal measurements campaign of ground-based aerosol optical depth for correlation with TOMS aerosol index.
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