# A bijection on core partitions and a parabolic quotient of the affine symmetric group

@article{Berg2009ABO, title={A bijection on core partitions and a parabolic quotient of the affine symmetric group}, author={Chris Berg and Brant C. Jones and Monica Vazirani}, journal={J. Comb. Theory, Ser. A}, year={2009}, volume={116}, pages={1344-1360} }

## 20 Citations

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## References

SHOWING 1-10 OF 14 REFERENCES

### Affine sl_p controls the representation theory of the symmetric group and related Hecke algebras

- Mathematics
- 1999

In this paper we prove theorems that describe how the representation theory of the affine Hecke algebra of type A and of related algebras such as the group algebra of the symmetric group are…

### Linear and Projective Representations of Symmetric Groups

- Mathematics
- 2005

Preface Part I. Linear Representations: 1. Notion and generalities 2. Symmetric groups I 3. Degenerate affine Hecke algebra 4. First results on Hn modules 5. Crystal operators 6. Character…

### CRANKS AND T -CORES

- Mathematics
- 1990

New statistics on partitions (called cranks) are defined which combinatorially prove Ramanujan’s congruences for the partition function modulo 5, 7, 11, and 25. Explicit bijections are given for the…

### The Representation Theory of the Symmetric Group

- Mathematics
- 2009

1. Symmetric groups and their young subgroups 2. Ordinary irreducible representations and characters of symmetric and alternating groups 3. Ordinary irreducible matrix representations of symmetric…

### Combinatorics of Coxeter Groups

- Mathematics
- 2005

I.- The basics.- Bruhat order.- Weak order and reduced words.- Roots, games, and automata.- II.- Kazhdan-Lusztig and R-polynomials.- Kazhdan-Lusztig representations.- Enumeration.- Combinatorial…

### 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.

### Blocks for symmetric groups and their covering groups and quadratic forms.

- Mathematics, Geology
- 1996

Introduction. Let p be a prime number, K a eld of characteristic p and let S n be the group of permu

### Ordering the Affine Symmetric Group

- Mathematics
- 2001

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

### 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.

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

- MathematicsJ. Comb. Theory, Ser. A
- 2005