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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 2014 to 2015
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:	not taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	prof. RNDr. Vladimír Souček, DrSc. doc. RNDr. Svatopluk Krýsl, Ph.D.
Class:	M Bc. OM M Bc. OM > Zaměření MSTR M Bc. OM > Doporučené volitelné
Classification:	Mathematics > Algebra

Annotation -

Last update: G_M (15.05.2012)

An elective course for specialization Mathematical structures within General Mathematics.

Literature - Czech

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

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.

Syllabus -

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

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.