On Kronecker Products of Spin Characters of the Double Covers of the Symmetric Groups

In recent years, a number of results on Kronecker products of complex Sncharacters have been obtained. In particular, the rectangular hull for the constituents in such products was found, and this was used for the classification of products with few homogeneous components; see [1] for this classification result and references to related work. Here, we provide similar results for products of spin characters for the double covers S̃n of the symmetric groups. The rectangular hull for spin products is determined in Theorem 3.2; this result serves as a crucial tool for the classification of homogeneous spin products in Theorem 4.2. (A module is called homogeneous if all of its composition factors are isomorphic to each other.) Finally, Theorem 4.2 is applied to prove a recent conjecture of Gow and Kleshchev describing certain homogeneous 2-modular tensor products for the symmetric groups (see Theorem 5.1).