# Tableaux on k+1-cores, reduced words for affine permutations, and k-Schur expansions

@article{Lapointe2005TableauxOK, title={Tableaux on k+1-cores, reduced words for affine permutations, and k-Schur expansions}, author={Luc Lapointe and Jennifer Morse}, journal={J. Comb. Theory, Ser. A}, year={2005}, volume={112}, pages={44-81} }

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## References

SHOWING 1-10 OF 23 REFERENCES

### Ordering the Affine Symmetric Group

- Mathematics
- 2001

We review several descriptions of the affine symmetric group. We explicit the basis of its Bruhat order.

### Schur function analogs for a filtration of the symmetric function space

- MathematicsJ. Comb. Theory, Ser. A
- 2003

### Tableau atoms and a new Macdonald positivity conjecture Duke Math J

- Engineering
- 2000

A snap action fluid control valve, the operation of which is controlled by a relatively slow acting thermally responsive actuator member. The valve of this invention is particularly adapted for use…

### Crystal base for the basic representation of $$U_q (\widehat{\mathfrak{s}\mathfrak{l}}(n))$$

- Mathematics
- 1990

AbstractWe show the existence of the crystal base for the basic representation of
$$U_q (\widehat{\mathfrak{s}\mathfrak{l}}(n))$$
by giving an explicit description in terms of Young diagrams.

### Algebraic Combinatorics And Quantum Groups

- Mathematics
- 2003

* Uno's Conjecture on Representation Types of Hecke Algebras (S Ariki) * Quiver Varieties, Afine Lie Algebras, Algebras of BPS States, and Semicanonical Basis (I Frenkel et al.) * Divided Differences…

### Crystal base for the basic representation of

- Mathematics
- 1990

We show the existence of the crystal base for the basic representation of Uq(~^l(n)) by giving an explicit description in terms of Young diagrams.

### Young Tableaux: With Applications to Representation Theory and Geometry

- Mathematics
- 1996

Part I. Calculus Of Tableux: 1. Bumping and sliding 2. Words: the plactic monoid 3. Increasing sequences: proofs of the claims 4. The Robinson-Schensted-Knuth Correspondence 5. The…

### Upper Bounds in Affine Weyl Groups under the Weak Order

- MathematicsOrder
- 1999

It is determined that the question of which pairs of elements of W have upper bounds can be reduced to the analogous question within a particular finite subposet within an affine Weyl group W0.