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At my university we are having a working group on perverse sheaves, with the aim of applying them to representation theory (Lusztig canonical bases for quivers/quantum groups etc). We are still lacking the idea of why we should be "naturally"interested in this. How would you motivate the appearance of these objects in representation theory and why one should be interested in this?

Another question would be maybe the historical developement of these ideas inside geometric representation theory.

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    $\begingroup$ I recommend Kleiman's article "The Development of Intersection Homology Theory" (PAMQ 2007), section 4. $\endgroup$
    – Piotr Achinger
    Commented Dec 7, 2021 at 13:03
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    $\begingroup$ It's better to have one question per question. Your second question is better suited for HSMSE. $\endgroup$
    – LSpice
    Commented Dec 7, 2021 at 15:34
  • $\begingroup$ I often find geometric constructions of representation theoretic objects more natural than purely algebraic constructions, but maybe that’s just me $\endgroup$
    – Exit path
    Commented Dec 7, 2021 at 18:57
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    $\begingroup$ @leibnewtz I often find algebraic constructions of representation theoretic objects more natural than purely geometric constructions, but maybe that’s just me :) $\endgroup$
    – Andrew
    Commented Dec 8, 2021 at 5:27

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