{'fraction_non_alphanumeric': 0.010183299389002037, 'fraction_numerical': 0.004073319755600814, 'mean_word_length': 4.72093023255814, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Character formulas on cohomology of deformations of Hilbert schemes of K3 surfaces

Let X be a hyperkähler manifold deformation equivalent to a Hilbert scheme of n points on a K3 surface. We compute the graded character formula of the generic Mumford–Tate group representation on the cohomology ring of X , and derive a generating series for deducing the number of canonical Hodge classes on X . The formula indicates the number of Hodge classes on X that remain Hodge under any deformation.