The level-restricted X=M fermionic formula conjecture

Let B0B_0, Br1,s1,,BrL,sLB^{r_1,s_1},\ldots,B^{r_L,s_L}, XlX_l, MlM_l, and the energy normalization cc satisfy the assumptions of the inhomogeneous X=M conjecture. Let ll be a positive integer.

Level-restricted X=M conjecture. One has

Xl(Br1,s1BrL,sL,0,q)=qcMl(Ws1(r1)WsL(rL),q),X_l(B^{r_1,s_1}\otimes\cdots\otimes B^{r_L,s_L},0,q) =q^cM_l(W^{(r_1)}_{s_1}\otimes\cdots\otimes W^{(r_L)}_{s_L},q),

where MlM_l is the level-restricted fermionic form defined in the source. This is the level-restricted analogue of the inhomogeneous X=M formula; the source gives no resolution status.

Sources & referencesView supporting material

Primary source

Goro Hatayama, Atsuo Kuniba, Masato Okado, Taichiro Takagi and Yasuhiko Yamada, “Remarks on Fermionic Formula”, arXiv:math/9812022 (1999).

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