2022-11-03

## Non-commutative symmetric functions

For an introduction to non-commutative symmetric functions, we refer to [GKLLRT95].

The non-commutative symmetric functions are dual to the quasisymmetric functions. These are not to be confused with symmetric functions in non-commutative variables.

## Non-commutative Schur functions

See [GKLLRT95] for definition of the non-commutative Schur polynomials.

## Murnaghan–Nakayama rule

See [Tew16] for a non-commutative lifting of the classical Murnaghan–Nakayama rule.

## References

- [GKLLRT95] Israel M. Gelfand, Daniel Krob, Alain Lascoux, Bernard Leclerc, Vladimir S. Retakh and Jean-Yves Thibon. Noncommutative symmetrical functions. Advances in Mathematics, 112(2):218–348, May 1995.
- [Tew16] Vasu Tewari. A Murnaghan–Nakayama rule for noncommutative Schur functions. European Journal of Combinatorics, 58:118–143, November 2016.