On the Cardinalities of Kronecker Quiver Grassmannians
نویسندگان
چکیده
Abstract. We deduce using the Ringel-Hall algebra approach explicit formulas for the cardinalities of some Grassmannians over a finite field associated to the Kronecker quiver. We realize in this way a quantification of the formulas obtained by Caldero and Zelevinsky for the Euler characteristics of these Grassmannians. We also present a recursive algorithm for computing the cardinality of every Kronecker quiver Grassmannian over a finite field.
منابع مشابه
On Quiver Varieties and Affine Grassmannians of Type A
We construct Nakajima’s quiver varieties of type A in terms of affine Grassmannians of type A. This gives a compactification of quiver varieties and a decomposition of affine Grassmannians into a disjoint union of quiver varieties. Consequently, singularities of quiver varieties, nilpotent orbits and affine Grassmannians are the same in type A. The construction also provides a geometric framewo...
متن کاملQuiver Varieties and Beilinson-drinfeld Grassmannians of Type A
We construct Nakajima’s quiver varieties of type A in terms of conjugacy classes of matrices and (non-Slodowy’s) transverse slices naturally arising from affine Grassmannians. In full generality quiver varieties are embedded into Beilinson-Drinfeld Grassmannians of type A. Our construction provides a compactification of Nakajima’s quiver varieties and a decomposition of an affine Grassmannian i...
متن کاملQuiver Grassmannians, Quiver Varieties and the Preprojective Algebra
Quivers play an important role in the representation theory of algebras, with a key ingredient being the path algebra and the preprojective algebra. Quiver grassmannians are varieties of submodules of a fixed module of the path or preprojective algebra. In the current paper, we study these objects in detail. We show that the quiver grassmannians corresponding to submodules of certain injective ...
متن کاملFramed Moduli and Grassmannians of Submodules
In this work we study a realization of moduli spaces of framed quiver representations as Grassmannians of submodules devised by Markus Reineke. Obtained is a generalization of this construction to finite dimensional associative algebras and for quivers with oriented cycles over an arbitrary infinite field. As an application we get an explicit realization of fibers for the moduli space bundle ov...
متن کاملBases of the Quantum Cluster Algebra of the Kronecker Quiver
We construct bar-invariant Z[q 1 2 ]−bases of the quantum cluster algebra of the Kronecker quiver which are quantum analogues of the canonical basis, semicanonical basis and dual semicanonical basis of the cluster algebra of the Kronecker quiver in the sense of [14],[4] and [11] respectively. As a byproduct, we prove the positivity of the elements in these bases.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009