Generalizations of Deodhar’s 𝛼-localization functor

Cox, Ben

doi:10.1090/S0002-9939-1994-1189540-5

Generalizations of Deodhar’s $\alpha$-localization functor
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by Ben Cox

Proc. Amer. Math. Soc. 121 (1994), 981-990

DOI: https://doi.org/10.1090/S0002-9939-1994-1189540-5

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Abstract:

In this paper we generalize the result of Deodhar (see Invent. Math. 57 (1980), 101-118) on $\alpha$-localization functors. Namely, we show that localization with respect to a larger family of left denominator sets "intertwines" with tensoring by finite-dimensional representations. In the language of the author’s previous work, localization with respect to such a left denominator set produces a new example of an $\mathfrak {F}$-functor and an $\mathfrak {F}$-category.

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