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by J Wan, W Wang

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Jinkui Wan, Weiqiang Wang
, 1201

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... of Hcn. Recall the authors [WW1] formulated earlier a spin coinvariant algebra for the algebra Hcn, and found a closed formula for the so-called spin fake degrees (this terminology appeared later in =-=[WW3]-=-). For a symmetric algebra H with a symmetrizing form, there exist elements called Schur elements (cf. [GP2, Theorem 7.2.1]) for irreducible characters, which can be used to determine when H is semsim...

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unknown authors

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...= 2 otherwise. Proof. Ignoring the grading shifts, the decomposition follows from multiplication of Schur Q-functions for two single row partitions. For more details on these formulas see for example =-=[WW]-=-. There is a degree zero isomorphism f : Sme(m) → Sme(m){1} where cǫ11 · · · c ǫm m e(m) 7→ c ǫ1 1 · · · c ǫm m (c1 + · · ·+ cm)e(m). This gives rise to a degree zero isomorphism F : Sm+n ⊗Sm×Sn (Sme(...

by
Jonathan Axtell

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...m|npλq may be decomposed as a double tableau tp1q|tp2q for standard tp1q P Tabm|0pµq and tp2q P Tab0|npλ{µq for some µ Ă λ. Hence, the result follows from (31) and (32). Recall from [Mac, Ch. III], =-=[WW]-=- the Hall-Littlewood symmetric function, Sλpx1, . . . , xnq “ hsλpx1, . . . , xn;x1, . . . , xnq “ ÿ µĂλ sµpx1, . . . , xmqsλ1{µ1px1, . . . , xnq, defined for λ P Λpnq. We then have the following. Cor...

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