?? second term as swing vote between "not induced" first term and "induced" third term ?? ... ??? ... accusing bump of using "induced" in peculiar way ?? ..... ??? trying to systematize / make more precise such peculiar and/or non-peculiar ways .... ?? "collection of all ways of seeing rep r as induced / quasi-induced" .... ?? and / or universal such .... ???? ...

?? maximal toruses in gl(3) ... trying to match up with kinds of irreps we seem to see in classification .... ??? young-diagrammatic flavor here ?? ....

?? q^3-1 ...

?? (q^2-1)(q-1) ...

?? (q-1)^3 ...

342*336*294 - (1^2 + 56^2 + 343^2)*6 - ((57*6)^2)*21*6 - (57^2 + (57*7)^2)*30 - ((57*8)^2)*20 =

33784128 - 724716 - 14737464 - 4873500 - 4158720 = 9289728 = 2^14 * 3^4 * 7


(q^3-1)*((q^2-1)(q-1))*((q-1)^3) = ??? .....

??? hmmm .... ??? _something_ being parameterized by "one character for "each" maximal torus" ????? ...... ????? .....

?? double life of these particular q-polynomials ... ?? well, or maybe triple, or single .... ???? .... ?? i was going to say "flag combinatorics vs ... this new (?? ...) stuff that we're doing now" ... ?? but ... maybe more unified, as to do with "factorization" of group gl(3) .... ???? ... ?? is there something about .... ???? subgroup pair of complementary index, with corresponding "decomposition" ??? ...

?? hmm, just remembering now that we didn't quite straighten out the q-polynomial for the cuspidal sector .... ???? ......