Timeline for In category O: weight spaces of tensor products
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 28, 2012 at 12:04 | comment | added | Jim Humphreys | @SH4pe: My wording was awkward. All I wanted to emphasize is that the grading on tensor products described by Konstantin is purely formal for graded vector spaces, but to apply it you have to know which tensor products of modules in the BGG category are actually in that category. In that category the most natural examples come from tensoring by finite dimensional modules. | |
| Mar 28, 2012 at 9:39 | comment | added | Sh4pe | @Humphreys: I don't understand how the direct sums in my case are finite and what you mean by finiteness. Do you mean that the summands are finite dimensional? Or that there are only finitely many summands? (The latter is not true in my case if I'm not mistaken...). Thank you! | |
| Mar 27, 2012 at 15:48 | comment | added | Jim Humphreys | @Konstantin: As you point out, the grading is a formal matter when you know that the direct sums involved are finite. While the original BGG category has strong finiteness conditions (assuring for instance existence of enough projectives), analogous categories for Kac-Moody algebras or quantum versions raise more challenging questions about the notion of tensoring. See for instance the 1993-1994 series of papers in J. Amer. Math. Soc. by Kazhdan & Lusztig on Tensor structures arising from affine Lie algebras. | |
| Mar 27, 2012 at 13:45 | vote | accept | Sh4pe | ||
| Mar 27, 2012 at 13:45 | comment | added | Sh4pe | Ah - right, thanks. That was much easier than expected :) | |
| Mar 27, 2012 at 10:45 | history | answered | user91132 | CC BY-SA 3.0 |