منابع مشابه
On the Deligne-Simpson problem
The Deligne-Simpson problem is formulated like this: give necessary and sufficient conditions for the choice of the conjugacy classes Cj ⊂ SL(n,C) or cj ⊂ sl(n,C) so that there exist irreducible (p + 1)-tuples of matrices Mj ∈ Cj or Aj ∈ cj satisfying the equality M1 . . .Mp+1 = I or A1 + . . .+Ap+1 = 0. We solve the problem for generic eigenvalues with the exception of the case of matrices Mj ...
متن کاملLecture 18: Deligne-simpson Problem
The Deligne-Simpson problem asks to find a condition on conjugacy classes C1, . . . , Ck ⊂ Matn(C) such that there are matrices Yi ∈ Ci with (1) ∑k i=1 Yi = 0, (2) and there are no proper subspaces in C stable under all Yi. Crawley-Boevey reduced this problem to checking if there is an irreducible representation in Rep(Π(Q), v) for suitable Q, λ, v produced from C1, . . . , Ck. Recall, Section ...
متن کاملThe Deligne-Simpson problem – a survey
The Deligne-Simpson problem (DSP) (resp. the weak DSP) is formulated like this: give necessary and sufficient conditions for the choice of the conjugacy classes Cj ⊂ GL(n,C) or cj ⊂ gl(n,C) so that there exist irreducible (resp. with trivial centralizer) (p + 1)-tuples of matrices Mj ∈ Cj or Aj ∈ cj satisfying the equality M1 . . .Mp+1 = I or A1+ . . .+Ap+1 = 0. The matrices Mj and Aj are inter...
متن کاملOn the Deligne-Simpson problem and its weak version
We consider the Deligne-Simpson problem (DSP) (resp. the weak DSP): Give necessary and sufficient conditions upon the choice of the p + 1 conjugacy classes cj ⊂ gl(n,C) or Cj ⊂ GL(n,C) so that there exist irreducible (p+ 1)-tuples (resp. (p+ 1)-tuples with trivial centralizers) of matrices Aj ∈ cj with zero sum or of matrices Mj ∈ Cj whose product is I. The matrices Aj (resp. Mj) are interprete...
متن کاملThe connectedness of some varieties and the Deligne-Simpson problem
The Deligne-Simpson problem (DSP) (resp. the weak DSP) is formulated like this: give necessary and sufficient conditions for the choice of the conjugacy classes Cj ⊂ GL(n,C) or cj ⊂ gl(n,C) so that there exist irreducible (resp. with trivial centralizer) (p + 1)-tuples of matrices Mj ∈ Cj or Aj ∈ cj satisfying the equality M1 . . .Mp+1 = I or A1+ . . .+Ap+1 = 0. The matrices Mj and Aj are inter...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Comptes Rendus de l'Académie des Sciences - Series I - Mathematics
سال: 1999
ISSN: 0764-4442
DOI: 10.1016/s0764-4442(00)88212-9