𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the Number of Absolutely Indecomposable Representations of a Quiver

✍ Scribed by Bert Sevenhant; Michel Van Den Bergh

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
147 KB
Volume
221
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

A conjecture of Kac states that the constant coefficient of the polynomial counting the number of absolutely indecomposable representations of a quiver over a finite field is equal to the multiplicity of the corresponding root in the associated Kac᎐Moody Lie algebra. In this paper we give a combinatorial reformulation of Kac's conjecture in terms of a property of q-multinomial coefficients. As a side result we give a formula for certain inverse Kostka᎐Foulkes polynomials.

πŸ“œ SIMILAR VOLUMES

On the Number of Injective Indecomposabl
On the Number of Injective Indecomposable Modules
✍ Hans-Heinrich Brungs; GΓΌnter TΓΆrner πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 158 KB

For every natural number m, there exists a noncommutative valuation ring R with a completely prime ideal P so that there are exactly m nonisomorphic indecomposable injective right R-modules with P as associated prime ideal.

On the Double of the Hall Algebra of a Q
On the Double of the Hall Algebra of a Quiver
✍ Bert Sevenhant; Michel Van den Bergh πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 181 KB

We show that it is possible to define reflection isomorphisms on the double of the (twisted) Hall algebra of a quiver. Combining these reflections with Fourier transform yields an alternative construction of Lusztig's braid group action on a quantum enveloping algebra.

On the Number of Integers Representable
On the Number of Integers Representable as Sums of Unit Fractions, III
✍ Hisashi Yokota πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 176 KB

Let NðnÞ be the set of all integers that can be expressed as a sum of reciprocals of distinct integers 4n: Then we prove that for sufficiently large n; which improves the lower bound given by Croot. # 2002 Elsevier Science (USA)