The Fine Moduli Space of Representations of Clifford Algebras
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, sa.15, ss.3524-3559, 2011 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2011
- Doi Numarası: 10.1093/imrn/rnq221
- Dergi Adı: INTERNATIONAL MATHEMATICS RESEARCH NOTICES
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.3524-3559
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
Given a fixed binary form f(u,v) of degree d over a field k, the associated Clifford algebra is the k-algebra C(f)=k{u,v}/I, where I is the two-sided ideal generated by elements of the form (alpha u+beta v)(d)-f(alpha,beta) with alpha and beta arbitrary elements in k. All representations of C(f) have dimensions that are multiples of d, and occur in families. In this article, we construct fine moduli spaces U=U(f,r) for the irreducible rd-dimensional representations of C(f) for each r >= 2. Our construction starts with the projective curve C subset of P(k)(2) defined by the equation w(d) = f(u, v), and produces U(f,r) as a quasiprojective variety in the moduli space M(r, d(r))of stable vector bundles over C with rank r and degree d(r)=r(d+g-1), where g denotes the genus of C.