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Let $V$ be a finite dimensional inner product space over $\mathbb{R}$ withdimension $n$, where $n\in \mathbb{N}$, $\wedge^{r}V$ be the exterior algebraof $V$, the problem is to find $\max_{\| \xi \| = 1, \| \eta \| = 1}\| \xi\wedge \eta \|$ where $k,l$ $\in \mathbb{N},$ $\forall \xi \in \wedge^{k}V,\eta \in \wedge^{l}V.$  This is a problem suggested by the famous Nobel Prize Winner C.N. Yang. Hesolved this problem for $k\leq 2$ in [1], and made the following\textbf{conjecture} in [2] : If $n=2m$, $k=2r$, $l=2s$, then the maximum isachieved when $\xi_{max} = \frac{\omega^{k}}{\| \omega^{k}\|}, \eta_{max} =\frac{\omega^{l}}{\| \omega^{l}\|}$, where $ \omega = \Sigma_{i=1}^me_{2i-1}\wedge e_{2i}, $ and $\{e_{k}\}_{k=1}^{2m}$ is an orthonormal basis ofV.  From a physicist's point of view, this problem is just the dual version ofthe easier part of the well-known Beauzamy-Bombieri inequality for product ofpolynomials in many variables, which is discussed in [4].  Here the duality is referred as the well known Bose-Fermi correspondence,where we consider the skew-symmetric algebra(alternative forms) instead of thefamiliar symmetric algebra(polynomials in many variables)  In this paper, for two cases we give estimations of the maximum of exteriorproducts, and the Yang's conjecture is answered partially under some specialcases.

On Maximum Norm of Exterior Product and A Conjecture of C.N. Yang