Let be a group and let be a graded representation of , i.e. a functor from to the category of graded vector spaces with each piece finite-dimensional. Thus acts on each graded piece individually, each of which is an ordinary finite-dimensional representation. We want to define a character associated to a graded representation, but if [...]
Archive for the ‘invariant theory’ Category
Introduction to symmetric functions
Posted in algebraic combinatorics, invariant theory, representation theory, tagged cycle indices, Hilbert series, representation theory of the symmetric group, symmetric functions on August 20, 2009 | 4 Comments »
The theory of symmetric functions, which generalizes some ideas that came up in the previous discussion of Polya theory, can be motivated by thinking about polynomial functions of the roots of a monic polynomial . Problems on high school competitions often ask for the sum of the squares or the cubes of the roots of [...]
-
Recent Comments
Qiaochu Yuan on The Yoneda lemma I Qiaochu Yuan on The Jacobson radical Joe Hannon on The Yoneda lemma I Amy Szczepanski on The Jacobson radical Qiaochu Yuan on The Yoneda lemma I -
Recent Posts
Categories
Archives
- May 2012
- April 2012
- March 2012
- February 2012
- January 2012
- December 2011
- November 2011
- October 2011
- August 2011
- July 2011
- June 2011
- April 2011
- March 2011
- February 2011
- January 2011
- December 2010
- November 2010
- October 2010
- September 2010
- August 2010
- July 2010
- June 2010
- May 2010
- April 2010
- March 2010
- February 2010
- January 2010
- December 2009
- November 2009
- October 2009
- September 2009
- August 2009
- July 2009
- June 2009
- May 2009
- April 2009
- January 2009
Tag Cloud
