The Hecke algebra $H_n$ can be described as the skein $R_n^n$ of $(n,n)$-tangle diagrams with respect to the framed Homfly relations. This algebra $R_n^n$ contains well-known idempotents $E_{\lambda}$ which are indexed by Young diagrams $\lambda$ with $n$ cells. The geometric closures $Q_{\lambda}$ of the $E_{\lambda}$ in the skein of the annulus are known to satisfy a combinatorial multiplication rule which is identical to the Littlewood–Richardson rule for Schur functions in the ring of symmetric functions. This fact is derived from two skein theoretic lemmas by using elementary determinantal arguments. Previously known proofs depended on results for quantum groups.