Nonvanishing of Kronecker Coefficients for Rectangular Shapes
نویسندگان
چکیده
We prove that for any partition (λ1, . . . , λd2) of size dm there exists k ≥ 1 such that the tensor square of the irreducible representation of the symmetric group Skdm with respect to the rectangular partition (km, . . . , km) contains the irreducible representation corresponding to the stretched partition (kλ1, . . . , kλd2). We also prove a related approximate version of this statement in which the stretching factor k is effectively bounded in terms of d. This investigation is motivated by questions of geometric complexity theory.
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تاریخ انتشار 2009