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Summary: Prof. Vlastimil Dlab (Carleton University, Ottawa):
REPRESENTATION THEORY AND
LINEAR ALGEBRA
I. a) A few historical remarks. Kronecker{Weierstrass pairs of matrices.
b) Valued graphs, their bilinear and quadratic forms, Weyl group, roots. Orienta-
tion, Coxeter transformations, defect, listing of roots.
c) K-realization (modulation and orientation) of valued graphs. The category
L(M;O) of their representations as a module category. Dimension vector, ba-
sic properties.
d) Coxeter functors C + and C . Relation to Auslander{Reiten translates. Prepro-
jective and preinjective representations, reltion to roots and their listing.
e) Characterization of nite representation type by Dynkin graphs.
II. a) Illustration of representations of Dynkin graphs. Von Staudt's pairs (of a real
and a complex subspace of a complex projective space).
b) Representations of Euclidean graphs of non-zero defect. Regular and homoge-
neous representations.
c) Regular representations of a non-simple realization of ~
A 12 .
d) Characterization of hereditary algebras of tame representation type by tame ten-
sor algebras (i.e. Euclidean graphs) and (exceptional) algebras A n ("; Ć).
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