7,628 research outputs found
Characters for Projective Modules in the BGG Category O for General Linear Lie Superalgebras
We determine the Verma multiplicities and the characters of projective
modules for atypical blocks in the BGG Category O for the general linear Lie
superalgebras and . We then explicitly
determine the composition factor multiplcities of Verma modules in the
atypicality 2 block of
Explicit Demazure character formula for negative dominant characters
In this paper, we prove that for any semisimple simply connected algebraic
group , for any regular dominant character of a maximal torus
of and for any element in the Weyl group , the character
is equal to
the sum of
the characters of dual of the top cohomology modules on the Schubert varieties
, running over all elements satisfying . Using this
result, we give a basis of the intersection of the Kernels of the Demazure
operators using the sums of the characters of
, where the sum is taken over all
elements in the Weyl group of .Comment: 11 page
Torus quotients of homogeneous spaces of the general linear group and the standard representation of certain symmetric groups
We give a stratification of the GIT quotient of the Grassmannian
modulo the normaliser of a maximal torus of with respect to the
ample generator of the Picard group of . We also prove that the flag
variety can be obtained as a GIT quotient of
modulo a maximal torus of for a suitable
choice of an ample line bundle on .Comment: 19 page
Association Rule Pruning based on Interestingness Measures with Clustering
Association rule mining plays vital part in knowledge mining. The difficult
task is discovering knowledge or useful rules from the large number of rules
generated for reduced support. For pruning or grouping rules, several
techniques are used such as rule structure cover methods, informative cover
methods, rule clustering, etc. Another way of selecting association rules is
based on interestingness measures such as support, confidence, correlation, and
so on. In this paper, we study how rule clusters of the pattern Xi - Y are
distributed over different interestingness measures.Comment: International Journal of Computer Science Issues, IJCSI Volume 6,
Issue 1, pp35-43, November 200
Nondegeneracy for Quotient Varieties under Finite Group Actions
We prove that for an abelian group of order the morphism defined by is
nondegenerate for every finite-dimensional representation of if and
only if either is a prime number or .Comment: 8 page
Projective normality of finite group quotients and EGZ theorem
In this note, we prove that for any finite dimensional vector space over
, and for a finite cyclic group , the projective variety
is projectively normal with respect to the descent of
by a method using toric variety, and deduce the
EGZ theorem as a consequence.Comment: 3 page
Torus quotients of homogeneous spaces-minimal dimensional Schubert Variety admitting semi-stable points
In this paper, for any simple, simply connected algebraic group of type
or and for any maximal parabolic subgroup of , we
describe all minimal dimensional Schubert varieties in admitting
semistable points for the action of a maximal torus with respect to an
ample line bundle on . In this paper, we also describe, for any
semi-simple simply connected algebraic group and for any Borel subgroup
of , all Coxeter elements for which the Schubert variety
admits a semistable point for the action of the torus with respect to a
non-trivial line bundle on
Projective normality of Weyl group quotients
In this note, we prove that for the standard representation of the Weyl
group of a semi-simple algebraic group of type
and over , the projective variety is
projectively normal with respect to the descent of , where denote the direct sum of copies of . We also prove
that for any finite group and for any finite dimentional representation
over , the projective variety is projectively normal with
respect to the descent of as a consequence.Comment: 10 page
Role of Interestingness Measures in CAR Rule Ordering for Associative Classifier: An Empirical Approach
Associative Classifier is a novel technique which is the integration of
Association Rule Mining and Classification. The difficult task in building
Associative Classifier model is the selection of relevant rules from a large
number of class association rules (CARs). A very popular method of ordering
rules for selection is based on confidence, support and antecedent size (CSA).
Other methods are based on hybrid orderings in which CSA method is combined
with other measures. In the present work, we study the effect of using
different interestingness measures of Association rules in CAR rule ordering
and selection for associative classifier
Syzygies of some GIT quotients
Let be flat scheme over such that its base change, , to
is Frobenius split for all primes . Let be a
reductive group scheme over acting on . In this paper, we prove
a result on the property for line bundles on GIT quotients of
for the action of . We apply our result to the
special cases of (1) an action of a finite group on the projective space and
(2) the action of a maximal torus on the flag variety of type .Comment: 11 pages; improved bounds in main results; new references adde
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