We prove that the local intersection cohomology of nilpotent orbit closures of cyclic quivers is trivial when the two orbits involved correspond to partitions with at most two rows. This gives a geometric proof of a result of Graham and Lehrer, which states that standard modules of the affine Hecke algebra of GLd corresponding to nilpotents with at most two Jordan blocks are multiplicity-free.

Abstract. The concept of Lagrange and Hermite interpolation polynomials can be generalized. The spectral basis of idempotents and nilpotents of a factor ring of polynomials provides a powerful framework for the expression of Lagrange and Hermite interpolation in 1, 2 and higher dimensional spaces. We give a new definition of quantum Lagrange and Hermite interpolation polynomials which works on ...

Let R be a ring with Jacobson radical J and with center C. Let P be the set of potent elements x for which xk = x for some integer k > 1. Let N be the set of nilpotents. A ring R is called subperiodic if R \ (J ∪ C) ⊆ N + P . We consider the commutativity behavior of a subperiodic ring with some constraint involving extended commutators. Mathematics Subject Classification: 16U80, 16D70

Remark 1.2. As a note on terminology, according to Milne, an affine variety over a field k is a variety isomorphic to the spectrum of a finitely generated k-algebra R such that R ⊗k k that has no nonzero nilpotents. A variety is a separated scheme admitting a covering by finitely many affine schemes [Mil, p. 5]. This is slightly different from Hartshorne’s definition; he requires the base field...