The shuffle conjecture for the character of diagonal coinvariants
The shuffle conjecture for the character of diagonal coinvariants
Fix and let . For a partition , let range over semistandard tableaux of skew shape , and let be the number of d-inversions defined from the diagonals of the tableau. Define
Here is the nabla operator on symmetric functions, is the elementary symmetric function, is the complete homogeneous symmetric function, and is the Hall inner product. The shuffle conjecture. One has
Equivalently, for every partition ,
This gives a tableau formula for the character of the diagonal coinvariant ring. The source presents it as the main conjecture; no resolution is stated in the supplied text.
Sources & referencesView supporting material
Primary source
J. Haglund, M. Haiman, N. Loehr, J. B. Remmel and A. Ulyanov, “A Combinatorial Formula for the Character of the Diagonal Coinvariants”, arXiv:math/0310424 (2004).
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