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Invariants of the Classical Groups - NMAG362

Title:	Klasické grupy a jejich invarianty
Guaranteed by:	Mathematical Institute of Charles University (32-MUUK)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2012 to 2012
Semester:	summer
E-Credits:	4
Hours per week, examination:	summer s.:2/1, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time

Guarantor:	prof. RNDr. Vladimír Souček, DrSc.
Teacher(s):	prof. RNDr. Vladimír Souček, DrSc.
Class:	M Bc. OM M Bc. OM > Zaměření MSTR M Bc. OM > Doporučené volitelné
Classification:	Mathematics > Algebra

Annotation -

An elective course for specialization Mathematical structures within General Mathematics.

Last update: G_M (15.05.2012)

Literature - Czech

R. Goodman, N. Wallach: Representation Theory and Invariants of Classical groups, Cambridge University Press, 2001.

S. Mukai: An introdution to Invariants and Moduli , Cambridge University Press, 2003.

Last update: Souček Vladimír, prof. RNDr., DrSc. (10.10.2012)

Syllabus -

Classical (linear) Lie groups and algebras. The Casimir operator, complete reducibility of their representations,

classification of finite dimensional irreducible representations, highest weight vectors.

Duality for representations of groups, the Schur-Weyl duality. Classical invariant theory, invariants of an action of Lie

groups and finite groups on vector spaces (e.g., on spaces of polynomials or tensors).

Applications in geometry, algebraic number theory, resp. applications in physics.

Last update: Souček Vladimír, prof. RNDr., DrSc. (13.09.2013)