arXiv subjects
Publications and source records attributed to K. N. Raghavan.
The main result of the paper is a determinantal formula for the restriction to a torus fixed point of the equivariant class of a Schubert subvariety in the torus equivariant integral cohomology ring of the Grassmannian. As a corollary, we obtain an equivariant version of the Giambelli formula.
Consider complex semisimple Lie algebras of a given dimension specified by their structure constants. We describe a finite collection of rational functions in the structure constants that form a complete set of invariants: two sets of structure constants determine isomorphic algebras if and only if each of these rational functions has the same value on the two sets. This collection is indexed by all chord diagrams with the number of chords being bounded by a function of the dimension.
Cohen Macaulay property of fiber cones of ideals is characterized in terms of its Hilbert series. Hilbert series of fiber cones of ideals with minimal mixed multiplicity is calculated. It is proved that the fiber cone of an m-primary ideal I with minimal mixed multiplicity is Cohen-Macaulay if and only if its reduction number is atmost one. Hilbert series of fiber cones of ideals generated by quadratic sequences in standard graded rings is computed by deforming it to a face ring of a simplicial complex. Applications are given to defining ideals of monomial projective space curves lying on the quadric xw-yz=0, straightening-closed ideals in graded algebras with straightening law and Huckaba-Huneke ideals of analytic spread 1 and 2.
We prove a recent conjecture of Kreiman and Lakshmibai about Hilbert functions of points on Schubert varieties in Grassmannians.
A unipotent triangular relationship is established between the dual standard monomial theoretic basis and canonical basis for the negative part of the quantized universal enveloping algebra of type A.