  The characters of the (total) Springer representations are identified with
the Green functions by Kazhdan [Israel J. Math. {\bf 28} (1977)], and the
latter are identified with Hall-Littlewood's $Q$-functions by Green [Trans.
Amer. Math. Soc. (1955)]. In this paper, we present a purely algebraic proof
that the (total) Springer representations of $\mathop{GL} ( n )$ are
$\mathrm{Ext}$-orthogonal to each other, and show that it is compatible with
the natural categorification of the ring of symmetric functions.

Representation Theory;Commutative Algebra;Combinatorics;Quantum Algebra