AI 中文总结
该研究计算扩展仿射Weyl群判别层的斋藤行列式，将Weyl分母公式因式分解推广到更高余维数层，得到Antoniou-Feigin-Strachan结果的q-模拟细化。
AI 中文摘要
我们研究扩展仿射Weyl群反射表示的商空间上的斋藤度量形式，该度量被限制在其判别式的任意层上。我们计算所有层和Dynkin型的斋藤行列式，证明其可被相关超平面排列的受限根的q-模拟的乘积整除。我们的结果同时将Weyl分母公式中的因式分解推广到更高余维数层，并为Coxeter群提供了Antoniou-Feigin-Strachan结果的q-模拟细化。
英文摘要
We investigate the form of the Saito metric on quotients of the reflection representation of an extended affine Weyl group, restricted to an arbitrary stratum of its discriminant. We compute the Saito determinant for all strata and Dynkin types and show that it is divisible by a product of q-analogues of restricted roots for the associated hyperplane arrangement. Our results simultaneously generalise the factorisation in the Weyl denominator formula to higher codimension strata, and provide q-analogue refinements of results of Antoniou-Feigin-Strachan for Coxeter groups.
Comments25 pages
