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.
The Hall Polynomials for Tame Quiver Algebras
โ Scribed by Shunhua Zhang
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 80 KB
- Volume
- 239
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
โฆ Synopsis
Let A be a finite-dimensional tame quiver algebra over a finite field k. We prove that Hall polynomials exist for A.
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Symmetric functions can be considered as operators acting on the ring of polynomials with coefficients in R. We present the package SFA, an implementation of this action for the computer algebra system Maple. As an example, we show how to recover different classical expressions of Lagrange inversion