[Giangibar]

First of all, I'm pointing out that the bidding is very far from natural (this board was played in the context of an artificial system with weak and transfer opening bids) but I'm writing it nonetheless because it has some consequences on the play.
In first seat, all red, you pick up ♠KQxx ♥xx ♦AJ87x ♣xx and decide to follow your system by opening 1♥ = 4+♠, could be canape, 9-14 points. LHO doubles, partner passes (showing tolerance for playing in Hearts), RHO passes too. You could just pass and sit in 1♥X, but you decide to follow the system and bid 2♦ = 4♠ and 5♦, minimum. LHO passes, partner passes (showing preference for Diamonds over Spades) and RHO bids 3♣. You pass, LHO bids 3NT, partner quickly doubles and the bidding ends. Partner leads the 4 of Diamonds (attitude, showing 1+ honors in Diamonds but no indication about suit length) and dummy comes on the table with ♠xx ♥xxx ♦10x ♣KQ109xx. Declarer seems disappointed and calls for a small Diamond. What do you play? The Jack, hoping to maintain communication with your partner in your likely running suit but risking to give declarer a free trick, or the Ace, winning the trick and preventing declarer from getting a trick he could be not entitled to, but maybe severing communications with partner?

[gnasher]

IMPs or matchpoints?

What did declarer's double of 1H show?

When partner passed 1H, what lengths in the majors do you expect, and what else could he have done?

[Giangibar]

The game was pairs, so match points. Declarer's double of 1♥ should have meant a takeout of a natural 1♠ opening, so 12+ HCP and 4♥, likely...

When partner passed 1♥X, he showed tolerance for playing in Hearts (maybe 4+ cards). Instead, he could have bid 1♠ as a relay to know my shape, XX as natural and penalty-oriented with about 11+ points and a flat shape, or 1NT/2♣/2♦ as a transfer for the next suit up with a weakish hand and 5-6+ cards. He could also have supported Spades with 3-4 cards. Partner's expected distribution is 1444 or 2533 or 2542 or 1543.