Schubert calculus studies the structural constants of the standard basis of the cohomology ring of the quantum Grassmannians. It is well known that it is isomorphic to the fusion ring of the category of finite-dimensional representations of the Lie algebra $\frak{gl}_n$. But you first discivered this isomorphism? Is it somehow obvious if you know the Littlewood--Richardson rules for $\frak{gl}_n$ irreps?
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asked Sep 18, 2022 at 15:20
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1$\begingroup$ Don't know for sure "who first discovered" this, but D. Peterson did a lot of unpublished work in the 90s on the quantum cohomology of Grassmannians and other flag varieties, and many foundational results are (at least partly) attributed to him. $\endgroup$– Sam HopkinsCommented Sep 18, 2022 at 15:24
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$\begingroup$ @Sam: Thanks for the comment, but I would guess this result was well-known even in the 90s . . . $\endgroup$– Didier de MontblazonCommented Sep 18, 2022 at 15:33
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$\begingroup$ But of course I could be wrong! $\endgroup$– Didier de MontblazonCommented Sep 18, 2022 at 15:45
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1$\begingroup$ Here's a '93 paper by Witten attributing the observation to Gepner. '91. arxiv.org/abs/hep-th/9312104 $\endgroup$– Allen KnutsonCommented Oct 9, 2022 at 21:43
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$\begingroup$ @AllenKnutson: Thanks a lot! $\endgroup$– Didier de MontblazonCommented Oct 12, 2022 at 9:04
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