# Questions tagged [schur-functions]

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### Is the appearance of Schur functions a coincidence?

The Schur functions are symmetric functions which appear in several different contexts: The characters of the irreducible representations for the symmetric group (under the characteristic isometry). ...
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### About Cauchy identity for Schur polynomials

(This was originally posted here, https://math.stackexchange.com/questions/4687466/cauchy-identity-for-schur-functions, and I am reposting it here as it seems to be more appropriate.) PRELIMINARY. The ...
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### Is it express in terms of Schur Q-function?

Consider next integral \begin{eqnarray} Z \ = \ h^{- N N_f} \ \int\limits_{SU(N)} \ dU \ \prod_{n=1}^{N} \ \det \left ( 1 + h U \right )^{ N_f} \ \left ( 1 + h U^{\dagger} \right )^{ N_f} \ = \sum_{...
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### Identities involving Littlewood–Richardson coefficients?

I am not aware of that many identities that involve several Littlewood–Richardson coefficients. One recent identity, is a generating function as sum of squares of LR-coefficients, due to Harris and ...
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### Evaluating derivatives of Schur polynomials

Given an arbitrary partition $\lambda$ and an integer $N$ (the number of variables), is there any further way to evaluate the following derivative of the Schur polynomial? \begin{align} A &= \...
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### An upper bound for a vector with given norm 1 and norm 2

Suppose $X = (x_1, \ldots , x_n)$ is given and we know that $x_i$'s are nonnegative, $\sum_{i=1}^n x_i = n$ and $\sum_{i=1}^n x_i^2 = m$. Just by this information, is it possible to find a vector ...
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### Is there a geometric interpretation of skew Schur functions?

Consider the cohomology ring of the Grassmannian of k-planes in complex n-space. It has a standard presentation as a quotient of the ring of symmetric functions. In this presentation, the Schur ...
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### Why do we care about Schur Positivity

Some of the most important open problems in Algebraic Combinatorics concern the Schur positivity of classes of symmetric functions. Why is this an important property to have?